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b(canja)22 b(jest)j(upra)m(v)m(o)f(nevjero)5 b(jatno)24 b(slaganje)f(teorijskih)g(predvid)p 3584 4610 V(anja)257 4843 y(i)32 b(eksp)s(erimen)m(talnih)g(rezultata.)404 5024 y(No)41 b(\(uvijek\))h(p)s(osto)5 b(je)41 b(pitanja)g(na)g(k)m(o)5 b(ja)42 b(ne)g(znamo)f(o)s(dgo)m(v)m(or)g(i)f(eksp)s(erimen)m(ti)i(k)m (o)5 b(je)42 b(ne)p 257 5117 1418 4 v 370 5178 a Fo(1)407 5208 y Fn(Originalni)54 b(izvje)l(\024)-37 b(sta)5 b(j)53 b(se)i(mo)n(\024)-39 b(ze)54 b(na)n(\023)-39 b(ci)53 b(na)i(stranici)f(Kraljevsk)n(e)49 b(\024)-37 b(sv)n(edsk)n(e)53 b(ak)-5 b(ademije)55 b(za)f(znanost)257 5358 y(h)n(ttp://www.nob)r (el.se/announcemen)n(t-99/ph)n(ysics99.h)n(tml.)2005 5674 y Ft(1)p eop %%Page: 2 5 2 4 bop 257 -89 a Fs(1.)44 b(UV)m(OD)3081 b Ft(2)257 294 y(znamo)50 b(ob)5 b(jasniti.)96 b(P)m(osto)5 b(je)52 b(parametri)d(u)h(Standardnom)g(Mo)s(delu)g(k)m(o)5 b(je)52 b(un)m(utar)f(njega)257 474 y(samog)41 b(ne)i(mo)m(\024)-46 b(zemo)41 b(o)s(drediti.)70 b(T)-8 b(eorija)41 b(gra)m(vitacije)g(se)f 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b(cin)27 b(opisujemo)g(samo)g(dio)g(faznog)p eop %%Page: 3 6 3 5 bop 257 -89 a Fs(1.)44 b(UV)m(OD)3081 b Ft(3)257 294 y(prostora,)44 b(o)s(dnosno)e(prediktivna)f(snaga)g(teorije)g(je)h (bitno)f(ograni)m(\024)-46 b(cena,)43 b(ali,)f(mo)m(\024)-46 b(zda)38 b(\024)-46 b(cak)42 b(i)257 474 y(v)-5 b(a)m(\024)-46 b(znije,)25 b(nemamo)d(p)s(otpun)m(u)i(sliku)e(teorije,)j(pa)e(nam)f (promi)m(\024)-46 b(cu)22 b(v)-5 b(a)m(\024)-46 b(zna)23 b(sv)m(o)5 b(jstv)-5 b(a)25 b(iste.)40 b(Izvrstan)257 655 y(primjer)25 b(za)h(to)f(su)i(relacije)e(dualnosti)f(k)m(o)5 b(je)27 b(p)s(o)m(v)m(ezuju)h(razli)m(\024)-46 b(cite)23 b(teorije)j(struna;)i(te)e(relacije)f(su)257 835 y(otkriv)m(ene)32 b(tek)g(u)f(razmatranjima)d(nep)s(erturbativne)k(strukture)h (\(solitonsk)-5 b(a)29 b(i)h(instan)m(tonsk)-5 b(a)257 1016 y(rje)g(\024)-44 b(senja\))29 b(teorije)d(struna.)43 b(Nadalje,)28 b(k)m(oriste)g(se)g(i)f(razne)h(nep)s(erturbativne)g (meto)s(de)g(i)e(v)m(e)m(\023)-46 b(c)29 b(p)s(o-)257 1197 y(stoje)m(\023)-46 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b(zb)s(og)i(v)m(eze)i(s)f(teorijom)d(struna)i(u)h (jedno)5 b(j)26 b(i)e(dvije)h(dimenzije)f([17].)41 b(Drugi)23 b(zanimljiv)2005 5674 y(6)p eop %%Page: 7 10 7 9 bop 257 -89 a Fs(2.)44 b(CALOGER)m(O-SUTHERLANDO)m(V)33 b(MODEL)1538 b Ft(7)257 294 y(mo)s(del,)38 b(tak)m(o)s(d)p 787 241 31 4 v(er)g(in)m(tenzivno)g(prou)m(\024)-46 b(ca)m(v)-5 b(an,)39 b(je)f(Haldane-Shastry)m(ev)h(spinski)f(lanac)e([18])i(k)m(o)5 b(ji)257 474 y(dobijemo)32 b(iz)h(Calogero)m(v)m(og)g(mo)s(dela)e(izb)s (orom)h(statisti)m(\024)-46 b(ck)m(og)32 b(parametra)h Fm(\025)28 b Ft(=)h(2.)46 b(Zanimljiv)-5 b(a)257 655 y(je)39 b(i)f(v)m(eza)h(Calogero-Sutherlando)m(v)m(og)f(mo)s(dela)e(s)j (dv)m(o)s(dimenzijsk)m(om,)g(anionsk)m(om)f(\014zik)m(om,)257 835 y(ali)31 b(o)h(tome)g(vi)-5 b(\024)-44 b(se)33 b(k)-5 b(asnije.)404 1016 y(U)31 b(o)m(v)m(om)h(p)s(ogla)m(vlju)27 b(\023)-46 b(cemo)31 b(se)h(up)s(oznati)f(s)h(k)m(olektivnom)f (teorijom)f(p)s(olja,)g(p)s(ono)m(vit)e(\023)-46 b(cemo)257 1197 y(nek)m(e)38 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Fg(\000)f Fh(x)2045 5141 y Fo(2)2083 5129 y Fn(\))692 5303 y Fh(\032)735 5269 y Fo(3)772 5303 y Fn(\()p Fh(x)p Fn(\))24 b(=)f(3)p Fh(\016)s Fn(\(0\))p Fh(\032)1226 5269 y Fo(2)1262 5303 y Fn(\()p Fh(x)p Fn(\))d Fg(\000)e Fn(2\()p Fh(\016)s Fn(\(0\)\))1728 5269 y Fo(2)1765 5303 y Fh(\032)p Fn(\()p Fh(x)p Fn(\))p Fh(:)p eop %%Page: 8 11 8 10 bop 257 -89 a Fs(2.)44 b(CALOGER)m(O-SUTHERLANDO)m(V)33 b(MODEL)1538 b Ft(8)257 294 y(funk)m(cionalne)40 b(v)m(eze)i(izmed)p 1265 241 31 4 v(u)d(p)s(olja)g(tak)m(o)s(d)p 1851 241 V(er)h(p)s(omi)m(\024)-46 b(cu)39 b(u)h(b)s(esk)m(ona)m(\024)-46 b(cnost,)44 b(te)c(no)m(v)m(e)i(v)-5 b(arijable)257 474 y(p)s(osta)5 b(ju)43 b(goto)m(v)m(o)g(neza)m(visne,)f(\024)-44 b(sto)43 b(omogu)m(\023)-46 b(cuje)43 b(de\014niranje)f(auten)m(ti)m (\024)-46 b(cne)44 b(teorije)e(p)s(olja)f(k)m(o)5 b(ja)257 655 y(opisuje)39 b(p)s(olazni)f(kv)-5 b(an)m(tnomehani)m(\024)-46 b(cki)38 b(sistem)h(u)g(danom)g(pribli)m(\024)-46 b(zenju.)61 b(Upra)m(v)m(o)40 b(je)f(to)g(k)m(ole-)257 835 y(ktivna)k(teorija)f(p)s (olja.)73 b(U)43 b(osno)m(vi,)j(sv)m(e)39 b(\024)-44 b(sto)44 b(radimo)d(je)i(netrivijalna)d(promjena)j(v)-5 b(arijabli,)257 1016 y(prijelaz)26 b(s)i Fm(N)38 b Ft(originalnih)24 b(stupnjev)-5 b(a)28 b(slob)s(o)s(de)f(na)g(no)m(vi)g(skup)i(b)s(esk)m (ona)m(\024)-46 b(cno)29 b(mnogo)d(v)-5 b(arijabli.)257 1438 y Fk(2.2)161 b(Kolektivna)55 b(form)l(ulacija)g(Calogero-)625 1712 y(Sutherlando)l(v)l(og)c(mo)t(dela)257 1991 y Ft(Calogero)m(v)22 b(mo)s(del,)g(k)m(o)5 b(ji)22 b(opisuje)f(sistem)h Fm(N)32 b Ft(nerelativisti)m(\024)-46 b(ckih)17 b(\024)-46 b(cestica)21 b(smje)-5 b(\024)-44 b(stenih)22 b(na)g(pra)m(v)m(cu,)257 2171 y(zadan)33 b(je)g(sljede)m(\023)-46 b(cim)31 b(hamiltonijanom:) 1239 2444 y Fm(H)36 b Ft(=)27 b Fp(\000)1566 2376 y Ft(\026)-50 b Fm(h)1621 2334 y Fr(2)p 1546 2421 135 4 v 1546 2512 a Ft(2)p Fm(m)1736 2336 y Fi(N)1707 2361 y Fj(X)1710 2543 y Fi(i)p Fr(=1)1881 2376 y Fm(@)1937 2340 y Fr(2)p 1854 2421 152 4 v 1854 2512 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Fr(2)1512 5232 y(0)1647 5210 y Ft(u)h(hamiltonijan)m(u)c(\(2.22\))i(vi) -5 b(\024)-44 b(se)39 b(ne)m(\023)-46 b(cemo)38 b(pisati,)h(ali)d(tre-) 257 5391 y(bamo)29 b(ga)g(imati)e(na)j(um)m(u)g(iz)f(dimenzijskih)f (razloga.)41 b(Sli)m(\024)-46 b(cno)29 b(k)-5 b(ao)29 b(i)g(u)h(Calogero)m(v)m(om)f(mo)s(delu,)p eop %%Page: 12 15 12 14 bop 257 -89 a Fs(2.)44 b(CALOGER)m(O-SUTHERLANDO)m(V)33 b(MODEL)1489 b Ft(12)257 294 y(zb)s(og)45 b(singularnosti)f (hamiltonijana)d(\(2.22\))k(u)g(to)m(\024)-46 b(ck)-5 b(ama)44 b Fm(')2580 309 y Fi(i)2658 294 y Ft(=)49 b Fm(')2847 309 y Fi(j)2883 294 y Ft(,)g(faktoriziramo)42 b(v)-5 b(aln)m(u)257 474 y(funk)m(ciju)33 b(na)g(slijede)m(\023)-46 b(ci)31 b(na)m(\024)-46 b(cin:)1300 755 y Fm( )31 b Ft(=)d(\001)1579 713 y Fi(\025)1625 755 y Fm(\036;)71 b Ft(\001)28 b(=)1996 671 y Fj(Y)1994 854 y Fi(i)p Ft(.)257 474 y(Dok)-5 b(az)44 b(relacije)f(\(2.41\))g(dobijemo)g(tak)m (o)c(\024)-44 b(sto)45 b(jednad)m(\024)-46 b(zbu)45 b(\(2.45\))f(za)g Fm(')3005 489 y 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Fi(x)3388 868 y Fm(')3452 883 y Fi(n)3499 868 y Ft(\()p Fm(x)p Ft(\))p 3293 912 338 4 v 3351 1003 a Fm(\032)3401 1018 y Fr(0)3441 1003 y Ft(\()p Fm(x)p Ft(\))3640 789 y Fj(!)3723 935 y Fm(:)3551 1116 y Ft(\(2.47\))257 1296 y(Napi)-5 b(\024)-44 b(simo)32 b(relaciju)g(\(2.47\))h(sa)h (zamijenjenim)d(indeksima)i Fm(m)h Ft(i)e Fm(n)p Ft(,)j(o)s(duzmimo)c (o)s(d)i(\(2.47\),)g(te)257 1477 y(parcijalno)e(in)m(tegrira)5 b(jmo,)25 b(\024)-44 b(sto)33 b(k)m(ona)m(\024)-46 b(cno)33 b(da)5 b(je)1336 1757 y(\()p Fm(!)1435 1772 y Fi(n)1504 1757 y Fp(\000)22 b Fm(!)1664 1772 y Fi(m)1731 1757 y Ft(\))1786 1640 y Fj(Z)1885 1757 y Fm(dx)2001 1690 y(')2065 1705 y Fi(n)2112 1690 y Ft(\()p Fm(x)p Ft(\))p Fm(')2307 1705 y Fi(m)2374 1690 y Ft(\()p Fm(x)p Ft(\))p 2001 1734 504 4 v 2142 1825 a Fm(\032)2192 1840 y Fr(0)2232 1825 y Ft(\()p Fm(x)p Ft(\))2543 1757 y(=)27 b(0)p Fm(:)829 b Ft(\(2.48\))257 2037 y(Vidimo)44 b(da)i(za)h Fm(n)k Fp(6)p Ft(=)f Fm(m)p Ft(,)g(in)m(tegral)45 b(mora)g(i)-5 b(\024)-44 b(s)m(\024)e(cezn)m(uti,)50 b(te)c(tak)m(o)h(dobijemo)e (relaciju)f(\(2.41\).)257 2218 y(Nadalje,)23 b(pretp)s(osta)m(vit)d (\023)-46 b(cemo)21 b(da)g(rje)-5 b(\024)-44 b(senja)23 b(jednad)m(\024)-46 b(zb)s(e)23 b(\(2.45\))d(uistin)m(u)i(zado)m(v)m (olja)m(v)-5 b(a)5 b(ju)21 b(relaciju)257 2398 y(p)s(otpunosti)32 b(\(2.42\),)27 b(\024)-44 b(sto)33 b(mo)m(\024)-46 b(zemo)31 b(i)h(k)-5 b(asnije)32 b(pro)m(vjeriti.)404 2579 y(P)m(otra)m(\024)-46 b(zimo)36 b(rje)-5 b(\024)-44 b(senje)40 b(jednad)m(\024)-46 b(zb)s(e)39 b(\(2.45\))e(u)h(obliku)f Fm(')2448 2594 y Fi(n)2495 2579 y Ft(\()p Fm(x)p Ft(\))g Fp(/)h Ft(exp)18 b(\()p Fp(\006)p Fm(inx)p Ft(\))q(.)60 b(Isk)m(oristimo)257 2759 y(izraz)32 b(za)h(F)-8 b(ouriero)m(v)32 b(transformat)f ("principal-)f(v)-5 b(alue")32 b(distribucije)1452 2972 y Fm(P)p 1376 3016 229 4 v 1376 3108 a(x)22 b Fp(\000)h Fm(y)1642 3040 y Ft(=)1772 2972 y(1)p 1755 3016 83 4 v 1755 3108 a(2)p Fm(i)1864 2923 y Fj(Z)1963 3040 y Fm(dk)s(e)2113 2999 y Fi(ik)r Fr(\()p Fi(x)p Fl(\000)p Fi(y)r Fr(\))2367 3040 y Ft(sign)o(\()p Fm(k)s Ft(\))p Fm(;)257 3320 y Ft(te)33 b(izra)m(\024)-46 b(cuna)5 b(jmo)257 3483 y Fj(Z)357 3600 y Fm(dy)479 3533 y(e)524 3497 y Fl(\006)p Fi(iny)p 469 3577 229 4 v 469 3668 a Fm(x)22 b Fp(\000)h Fm(y)790 3600 y Ft(=)976 3533 y(1)p 959 3577 83 4 v 959 3668 a(2)p Fm(i)1068 3483 y Fj(Z)1167 3600 y Fm(dk)31 b(dy)f(e)1474 3559 y Fi(i)p Fr(\()p Fl(\006)p Fi(n)p Fl(\000)p Fi(k)r Fr(\))p Fi(y)1786 3600 y Fm(e)1831 3559 y Fi(ik)r(x)1937 3600 y Ft(sign\()p Fm(k)s Ft(\))e(=)f Fp(\000)p Fm(i\031)2553 3483 y Fj(Z)2653 3600 y Fm(dk)j(\016)t Ft(\()p Fp(\006)p Fm(n)23 b Fp(\000)g Fm(k)s Ft(\))28 b Fm(e)3293 3559 y Fi(ik)r(x)3399 3600 y Ft(sign\()p Fm(k)s Ft(\))f(=)790 3806 y(=)83 b Fp(\007)p Fm(i\031)t Ft(sign\()p Fm(n)p Ft(\))28 b Fm(e)1494 3764 y Fl(\006)p Fi(inx)1660 3806 y Fm(:)1893 b Ft(\(2.49\))257 4086 y(Uvrstimo)40 b(dobiv)m(eni)g(rezultat)g(u)g(jednad)m(\024)-46 b(zbu)42 b(\(2.45\),)g(te)e(k)m(ona)m(\024)-46 b(cno)42 b(uzmimo)c(u)i(obzir)g (da)h(je)257 4266 y(na)-5 b(\024)-44 b(se)34 b(stati)m(\024)-46 b(ck)m(o)32 b(rje)-5 b(\024)-44 b(senje)34 b(minimalne)29 b(energije)j(k)m(onstan)m(ta,)i(tj.)43 b Fm(\032)2691 4281 y Fr(0)2731 4266 y Ft(\()p Fm(x)p Ft(\))28 b(=)g Fm(\032)3044 4281 y Fr(0)968 4547 y Fm(!)1029 4562 y Fi(n)1075 4547 y Fm(')1139 4562 y Fi(n)1186 4547 y Ft(\()p Fm(x)p Ft(\))g(=)1459 4479 y Fm(\025)22 b Fp(\000)g Ft(1)p 1459 4523 228 4 v 1548 4615 a(2)1696 4547 y Fm(@)1752 4505 y Fr(2)1747 4571 y Fi(x)1793 4547 y Fm(')1857 4562 y Fi(n)1903 4547 y Ft(\()p Fm(x)p Ft(\))h Fp(\007)g Fm(i\031)t (\025\032)2356 4562 y Fr(0)2395 4547 y Ft(sign\()p Fm(n)p Ft(\))28 b Fm(@)2777 4562 y Fi(x)2821 4547 y Fm(')2885 4562 y Fi(n)2932 4547 y Ft(\()p Fm(x)p Ft(\))p Fm(;)461 b Ft(\(2.50\))252 4827 y(\024)-44 b(sto)47 b(nak)m(on)g(deriviranja)e (da)5 b(je)46 b(izraz)g(za)g(vlastite)g(frekv)m(encije)i(malih)43 b(oscilacija,)48 b(o)s(dnosno)257 5007 y(disp)s(erzijsku)33 b(funk)m(ciju)g Fm(!)1227 5022 y Fi(n)1274 5007 y Ft(:)1465 5288 y Fm(!)1526 5303 y Fi(n)1600 5288 y Ft(=)28 b Fp(\000)1791 5220 y Fm(\025)23 b Fp(\000)f Ft(1)p 1791 5264 V 1881 5356 a(2)2029 5288 y Fm(n)2087 5246 y Fr(2)2149 5288 y Ft(+)g Fm(\031)t(\025\032)2413 5303 y Fr(0)2452 5288 y Fp(j)p Fm(n)p Fp(j)p Fm(:)958 b Ft(\(2.51\))p eop %%Page: 17 20 17 19 bop 257 -89 a Fs(2.)44 b(CALOGER)m(O-SUTHERLANDO)m(V)33 b(MODEL)1489 b Ft(17)404 294 y(V)-8 b(ratimo)37 b(se)j(na)f(tren)m (utak)i(hamiltonijan)m(u)36 b(\(2.43\),)k(to)m(\024)-46 b(cnije)39 b(na)g(dv)-5 b(a)39 b(p)s(osljednja,)i(div)m(er-)257 474 y(gen)m(tna)31 b(\024)-46 b(clana.)42 b(P)m(ok)-5 b(azat)30 b(\023)-46 b(cemo)32 b(da)h(se)g(oni)f(to)m(\024)-46 b(cno)32 b(p)s(oni)-5 b(\024)-44 b(sta)m(v)-5 b(a)5 b(ju)32 b(s)h(v)-5 b(akuumsk)m(om)33 b(energijom:)1643 755 y Fm(E)1715 770 y Fi(v)r(ac)1852 755 y Ft(=)1965 687 y Fp(h)p Ft(0)p Fp(j)p Fm(H)2170 651 y Fr(\(2\))2263 687 y Fp(j)p Ft(0)p Fp(i)p 1965 731 414 4 v 2070 823 a(h)p Ft(0)p Fp(j)p Ft(0)p Fp(i)2388 755 y Fm(:)1136 b Ft(\(2.52\))257 1035 y(V)-8 b(akuumsk)m(o)34 b(stanje)f(op)s(eratora)f Fm(H)40 b Ft(\(2.43\))31 b(dano)i(je)g(izrazom:)1487 1315 y Fp(j)p Ft(0)p Fp(i)27 b Ft(=)g(exp)1899 1169 y Fj( )1965 1315 y Fp(\000)2052 1248 y Ft(1)p 2052 1292 49 4 v 2052 1383 a(2)2127 1232 y Fj(X)2166 1406 y Fi(n)2264 1315 y Fm(!)2325 1330 y Fi(n)2372 1315 y Fm(q)2419 1274 y Fr(2)2415 1340 y Fi(n)2462 1169 y Fj(!)2544 1315 y Fm(:)980 b Ft(\(2.53\))257 1595 y(T)-8 b(o)33 b(mo)m(\024)-46 b(zemo)31 b(izraziti)g(p)s(omo)m(\023)-46 b(cu)31 b(p)s(olja)38 b(~)-56 b Fm(\021)t Ft(\()p Fm(x)p Ft(\))33 b(k)m(oriste)m(\023)-46 b(ci)32 b(in)m(v)m(erzan)i(izraz)e(relaciji)e(\(2.38\))1548 1875 y Fm(q)1591 1890 y Fi(n)1666 1875 y Ft(=)1770 1758 y Fj(Z)1869 1875 y Fm(dx)7 b Ft(~)-56 b Fm(\021)t Ft(\()p Fm(x)p Ft(\))2199 1808 y Fm(')2263 1823 y Fi(n)2310 1808 y Ft(\()p Fm(x)p Ft(\))p 2168 1852 305 4 v 2168 1869 a Fj(q)p 2252 1869 222 4 v 2252 1969 a Fm(\032)2302 1984 y Fr(0)2341 1969 y Ft(\()p Fm(x)p Ft(\))2483 1875 y Fm(;)1041 b Ft(\(2.54\))257 2197 y(i)32 b(jo)-5 b(\024)-44 b(s)33 b(p)s(o)5 b(jednosta)m(vniti)32 b(k)m(oriste)m(\023)-46 b(ci)32 b(jednad)m(\024)-46 b(zbu)34 b(\(2.45\).)43 b(Kona)m(\024)-46 b(cno)32 b(imamo:)1125 2478 y Fp(j)p Ft(0)p Fp(i)27 b Ft(=)h(exp)1537 2356 y Fj(\022)1598 2478 y Fp(\000)1685 2410 y Ft(1)p 1685 2454 49 4 v 1685 2546 a(4)1761 2360 y Fj(Z)1861 2478 y Fm(dxdy)t(\021)t Ft(\()p Fm(x)p Ft(\))p Fm(G)2330 2436 y Fl(\000)p Fr(1)2423 2478 y Ft(\()p Fm(x;)17 b(y)t Ft(\))p Fm(\021)t Ft(\()p Fm(y)t Ft(\))2830 2356 y Fj(\023)2906 2478 y Fm(;)618 b Ft(\(2.55\))257 2758 y(gdje)33 b(je)g Fm(G)649 2722 y Fl(\000)p Fr(1)743 2758 y Ft(\()p Fm(x;)17 b(y)t Ft(\))32 b(in)m(v)m(erz)h(k)m(orelacijsk)m(e)g (funk)m(cije,)g(dan)g(izrazom)1062 3038 y Fm(G)1139 2997 y Fl(\000)p Fr(1)1234 3038 y Ft(\()p Fm(x;)17 b(y)t Ft(\))26 b(=)i Fp(\000)p Ft(2)p Fm(\025)17 b Ft(ln)f Fp(j)p Fm(x)22 b Fp(\000)h Fm(y)t Fp(j)e(\000)h Ft(\()p Fm(\025)g Fp(\000)h Ft(1\))2608 2971 y Fm(\016)t Ft(\()p Fm(x)f 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Ft(\(2.57\))257 4059 y(Sada)33 b(je)g(p)s(otpuni)e (hamiltonijan)e(dan)k(izrazom)1569 4339 y Fm(H)j Ft(=)27 b Fm(E)1861 4354 y Fr(0)1923 4339 y Ft(+)2021 4256 y Fj(X)2059 4431 y Fi(n)2157 4339 y Fm(!)2218 4354 y Fi(n)2265 4339 y Fm(a)2316 4298 y Fl(y)2316 4364 y Fi(n)2363 4339 y Fm(a)2414 4354 y Fi(n)2462 4339 y Fm(;)1062 b Ft(\(2.58\))257 4620 y(gdje)33 b(smo)f(uv)m(eli)g(standardne)i(b)s(ozonsk)m(e)g(op)s (eratore)e(stv)-5 b(aranja)32 b(i)g(p)s(oni)-5 b(\024)-44 b(stenja)1388 4900 y Fm(a)1439 4859 y Fl(y)1439 4924 y Fi(n)1514 4900 y Ft(=)1669 4832 y(1)p 1627 4877 132 4 v 1627 4894 a Fp(p)p 1710 4894 49 4 v 82 x Ft(2)1786 4754 y Fj( )1851 4831 y Fp(p)p 1934 4831 108 4 v 69 x Fm(!)1995 4915 y Fi(n)2042 4900 y Fm(q)2085 4915 y Fi(n)2154 4900 y Fp(\000)2343 4832 y Fm(i)p 2264 4877 191 4 v 2264 4904 a Fp(p)p 2347 4904 108 4 v 64 x Fm(!)2408 4983 y Fi(n)2465 4900 y Fm(p)2514 4915 y Fi(n)2561 4754 y Fj(!)2643 4900 y Fm(;)881 b Ft(\(2.59\))1389 5257 y Fm(a)1440 5272 y Fi(n)1515 5257 y Ft(=)1670 5190 y(1)p 1628 5234 132 4 v 1628 5252 a Fp(p)p 1711 5252 49 4 v 82 x Ft(2)1786 5111 y Fj( )1852 5188 y Fp(p)p 1935 5188 108 4 v 69 x Fm(!)1996 5272 y Fi(n)2043 5257 y Fm(q)2086 5272 y Fi(n)2155 5257 y Ft(+)2342 5190 y Fm(i)p 2263 5234 191 4 v 2263 5262 a Fp(p)p 2346 5262 108 4 v 64 x Fm(!)2407 5341 y Fi(n)2464 5257 y Fm(p)2513 5272 y Fi(n)2560 5111 y Fj(!)2642 5257 y Fm(:)h Ft(\(2.60\))p eop %%Page: 18 21 18 20 bop 257 -89 a Fs(2.)44 b(CALOGER)m(O-SUTHERLANDO)m(V)33 b(MODEL)1489 b Ft(18)404 294 y(Sada)35 b(\023)-46 b(cemo)38 b(izv)m(esti)g(disp)s(erzijsku)g(relaciju)f(za)h(Sutherlondo)m(v)h(mo)s (del,)f(na)g(malo)e(jedno-)257 474 y(sta)m(vniji)e(na)m(\024)-46 b(cin.)50 b(Od)35 b(p)s(o)m(\024)-46 b(cetk)-5 b(a)32 b(\023)-46 b(cemo)34 b(uzeti)h(u)f(obzir)h(da)f(razvijamo)f(gusto)m (\023)-46 b(cu)36 b Fm(\032)p Ft(\()p Fm(')p Ft(\))e(ok)m(o)h(k)m(on-) 257 655 y(stan)m(tnog)e(rje)-5 b(\024)-44 b(senja)33 b Fm(\032)1064 670 y Fr(0)1104 655 y Ft(.)44 b(U)32 b(tom)g(slu)m(\024) -46 b(ca)5 b(ju)33 b(hamiltonijan)28 b(kv)-5 b(adrati)m(\024)-46 b(can)33 b(u)f(p)s(olju)g Fm(\021)t Ft(\()p Fm(')p Ft(\))g(je)301 941 y Fm(H)390 900 y Fr(\(2\))511 941 y Ft(=)625 874 y(1)p 625 918 49 4 v 625 1009 a(2)684 941 y Fm(\032)734 956 y Fr(0)790 824 y Fj(Z)890 941 y Fm(d')p Ft(\()p Fm(@)1094 956 y Fi(')1144 941 y Fm(\031)t Ft(\()p Fm(')p Ft(\)\))1381 900 y Fr(2)1442 941 y Ft(+)1550 874 y(1)p 1550 918 V 1550 1009 a(2)1609 941 y Fm(\032)1659 956 y Fr(0)1715 824 y Fj(Z)1815 941 y Fm(d')1947 795 y Fj( )2021 874 y Fm(\025)22 b Fp(\000)h Ft(1)p 2021 918 228 4 v 2066 1009 a(2)p Fm(\032)2165 1024 y Fr(0)2259 941 y Fm(@)2310 956 y Fi(')2360 941 y Fm(\021)t Ft(\()p Fm(')p Ft(\))f(+)2682 874 y Fm(\025)p 2682 918 57 4 v 2686 1009 a Ft(2)2749 941 y Fp(\000)2748 824 y Fj(Z)2832 941 y Fm(d')2947 900 y Fl(0)2969 941 y Ft(ctg)3111 874 y Fm(')g Fp(\000)g Fm(')3360 837 y Fl(0)p 3111 918 273 4 v 3223 1009 a Ft(2)3394 941 y Fm(\021)t Ft(\()p Fm(')3548 900 y Fl(0)3570 941 y Ft(\))3608 795 y Fj(!)3674 818 y Fr(2)3730 941 y Fm(:)3551 1122 y Ft(\(2.61\))257 1302 y(Uv)m(edimo)33 b(op)s(eratore)775 1570 y Fm(A)p Ft(\()p Fm(')p Ft(\))27 b(=)h Fm(@)1170 1585 y Fi(')1221 1570 y Fm(\031)t Ft(\()p Fm(')p Ft(\))21 b(+)h Fm(i)1589 1423 y Fj(")1648 1502 y Fm(\025)g Fp(\000)g Ft(1)p 1648 1546 228 4 v 1692 1638 a(2)p Fm(\032)1791 1653 y Fr(0)1885 1570 y Fm(@)1936 1585 y Fi(')1987 1570 y Fm(\021)t Ft(\()p Fm(')p Ft(\))f(+)2308 1502 y Fm(\025)p 2308 1546 57 4 v 2312 1638 a Ft(2)2375 1570 y Fp(\000)2374 1452 y Fj(Z)2458 1570 y Fm(d')2573 1528 y Fl(0)2596 1570 y Ft(ctg)2737 1502 y Fm(')h Fp(\000)h Fm(')2987 1466 y Fl(0)p 2737 1546 273 4 v 2849 1638 a Ft(2)3020 1570 y Fm(\021)t Ft(\()p Fm(')3174 1528 y Fl(0)3197 1570 y Ft(\))3235 1423 y Fj(#)3551 1570 y Ft(\(2.62\))756 1914 y Fm(A)829 1873 y Fl(y)865 1914 y Ft(\()p Fm(')p Ft(\))k(=)h Fm(@)1187 1929 y Fi(')1238 1914 y Fm(\031)t Ft(\()p Fm(')p Ft(\))21 b Fp(\000)i Fm(i)1608 1768 y Fj(")1666 1846 y Fm(\025)f Fp(\000)h Ft(1)p 1666 1891 228 4 v 1711 1982 a(2)p Fm(\032)1810 1997 y Fr(0)1904 1914 y Fm(@)1955 1929 y Fi(')2005 1914 y Fm(\021)t Ft(\()p Fm(')p Ft(\))f(+)2327 1846 y Fm(\025)p 2327 1891 57 4 v 2331 1982 a Ft(2)2394 1914 y Fp(\000)2393 1797 y Fj(Z)2476 1914 y Fm(d')2591 1873 y Fl(0)2614 1914 y Ft(ctg)2756 1846 y Fm(')g Fp(\000)g Fm(')3005 1810 y Fl(0)p 2756 1891 273 4 v 2868 1982 a Ft(2)3039 1914 y Fm(\021)t Ft(\()p Fm(')3193 1873 y Fl(0)3215 1914 y Ft(\))3253 1768 y Fj(#)3551 1914 y Ft(\(2.63\))255 2143 y(\024)-46 b(ciji)30 b(je)j(k)m(om)m(utator)834 2410 y([)p Fm(A)p Ft(\()p Fm(')p Ft(\))p Fm(;)17 b(A)1191 2369 y Fl(y)1226 2410 y Ft(\()p Fm(')1328 2369 y Fl(0)1352 2410 y Ft(\)])27 b(=)h Fp(\000)1635 2343 y Fm(\025)22 b Fp(\000)h Ft(1)p 1635 2387 228 4 v 1704 2479 a Fm(\032)1754 2494 y Fr(0)1873 2410 y Fm(@)1924 2425 y Fi(')1974 2410 y Fm(@)2025 2425 y Fi(')2071 2406 y Fe(0)2098 2410 y Fm(\016)t Ft(\()p Fm(')f Fp(\000)h Fm(')2433 2369 y Fl(0)2456 2410 y Ft(\))f(+)g Fm(\025@)2722 2425 y Fi(')2773 2410 y Ft(ctg)2914 2343 y Fm(')g Fp(\000)h Fm(')3164 2307 y Fl(0)p 2914 2387 273 4 v 3026 2479 a Ft(2)3197 2410 y Fm(:)327 b Ft(\(2.64\))257 2678 y(Hamiltonijan)29 b(\(2.26\))j(sad)h (mo)m(\024)-46 b(zemo)31 b(napisati)g(u)i(obliku)811 2945 y Fm(H)i Ft(=)27 b Fm(E)1102 2960 y Fr(0)1164 2945 y Ft(+)1272 2878 y Fm(\032)1322 2893 y Fr(0)p 1272 2922 90 4 v 1292 3014 a Ft(2)1388 2828 y Fj(Z)1488 2945 y Fm(d'A)1676 2904 y Fl(y)1711 2945 y Ft(\()p Fm(')p Ft(\))p Fm(A)p Ft(\()p Fm(')p Ft(\))22 b(+)2194 2878 y Fm(\032)2244 2893 y Fr(0)p 2194 2922 V 2214 3014 a Ft(4)2310 2828 y Fj(Z)2410 2945 y Fm(d')p Ft([)p Fm(A)p Ft(\()p Fm(')p Ft(\))p Fm(;)17 b(A)2882 2904 y Fl(y)2917 2945 y Ft(\()p Fm(')p Ft(\)])811 3189 y Fp(\000)898 3122 y Fm(\025)22 b Fp(\000)h Ft(1)p 898 3166 228 4 v 987 3257 a(4)1152 3072 y Fj(Z)1252 3189 y Fm(d'@)1423 3148 y Fr(2)1418 3214 y Fi(')1468 3189 y Fm(\016)t Ft(\()p Fm(')f Fp(\000)g Fm(')1802 3148 y Fl(0)1826 3189 y Ft(\))p Fp(j)1892 3204 y Fi(')p Fr(=)p Fi(')2039 3185 y Fe(0)2087 3189 y Fp(\000)2196 3122 y Fm(\025)p 2196 3166 57 4 v 2200 3257 a Ft(4)2263 3189 y Fm(\032)2313 3204 y Fr(0)2369 3072 y Fj(Z)2469 3189 y Fm(d'@)2635 3204 y Fi(')2685 3189 y Ft(ctg)2827 3122 y(\()p Fm(')g Fp(\000)g Fm(')3114 3086 y Fl(0)3138 3122 y Ft(\))p 2827 3166 349 4 v 2977 3257 a(2)3185 3189 y Fp(j)3213 3204 y Fi(')p Fr(=)p Fi(')3360 3185 y Fe(0)3386 3189 y Fm(;)138 b Ft(\(2.65\))257 3457 y(gdje)48 b(je)g Fm(E)674 3472 y Fr(0)761 3457 y Ft(energija)f(osno)m(vnog)i(p)s(obud)p 1814 3404 31 4 v(enja)f(dana)f(izrazom)f(\(2.33\).)88 b(Lak)m(o)48 b(se)h(mo)m(\024)-46 b(zemo)257 3637 y(uvjeriti)34 b(da)h(k)m(om)m(utator)f(\(2.64\))h(u)g(slu)m(\024)-46 b(ca)5 b(ju)35 b Fm(')1989 3601 y Fl(0)2043 3637 y Fp(!)d Fm(')i Ft(to)m(\024)-46 b(cno)35 b(krati)f(div)m(ergen)m(tne)j (doprinose)d(u)257 3818 y(hamiltonijan)m(u)c(\(2.65\),)i(i)f(k)m(ona)m (\024)-46 b(cno)33 b(da)5 b(je)1364 4085 y Fm(H)36 b Ft(=)27 b Fm(E)1656 4100 y Fr(0)1718 4085 y Ft(+)1826 4018 y(1)p 1826 4062 49 4 v 1826 4154 a(2)1885 4085 y 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Ft(\))p Fm(a)2851 4853 y Fl(y)2851 4919 y Fi(n)2898 4894 y Fm(;)626 b Ft(\(2.67\))257 5123 y(k)m(o)5 b(ji)33 b(zado)m(v)m(olja)m (v)-5 b(a)5 b(ju)32 b(uobi)m(\024)-46 b(ca)5 b(jene)33 b(b)s(ozonsk)m(e)i(k)m(om)m(utacijsk)m(e)e(relacije)1188 5391 y([)p Fm(a)1266 5406 y Fi(n)1313 5391 y Fm(;)17 b(a)1408 5350 y Fl(y)1408 5416 y Fi(m)1475 5391 y Ft(])27 b(=)h Fm(\016)1676 5406 y Fi(n;m)1833 5391 y Fm(;)44 b Ft([)p Fm(a)1982 5406 y Fi(n)2029 5391 y Fm(;)17 b(a)2124 5406 y Fi(m)2191 5391 y Ft(])28 b(=)f([)p Fm(a)2427 5350 y Fl(y)2427 5416 y Fi(n)2475 5391 y Fm(;)17 b(a)2570 5350 y Fl(y)2570 5416 y Fi(m)2636 5391 y Ft(])28 b(=)f(0)p Fm(:)681 b Ft(\(2.68\))p eop %%Page: 19 22 19 21 bop 257 -89 a Fs(2.)44 b(CALOGER)m(O-SUTHERLANDO)m(V)33 b(MODEL)1489 b Ft(19)257 294 y(Zah)m(tjev)-5 b(amo)50 b(da)g(hamiltonijan)d(\(2.66\))j(bude)h(dijagonalan)d(u)j(tim)d(no)m (vim)i(op)s(eratorima,)257 474 y(o)s(dnosno)33 b(da)f(vrijedi:)1685 655 y Fm(H)k Ft(=)1905 572 y Fj(X)1944 746 y Fi(n)2042 655 y Fm(!)2103 670 y Fi(n)2149 655 y Fm(a)2200 614 y Fl(y)2200 680 y Fi(n)2247 655 y Fm(a)2298 670 y Fi(n)2346 655 y Fm(:)1178 b Ft(\(2.69\))257 885 y(U)35 b(gornjim)e(izrazima)g(u)i (slu)m(\024)-46 b(ca)5 b(ju)35 b(k)m(on)m(tin)m(uiranog)f(sp)s(ektra,)j (sum)m(u)e(u)h(izrazu)e(\(2.69\))g(zamjen-)257 1065 y(jujemo)41 b(in)m(tegralom.)67 b(Uvrstimo)40 b(sad)i(razv)m(o)5 b(j)42 b(\(2.67\))e(u)h(k)m(om)m(utacijsku)h(relaciju)e(\(2.64\),)i(te) 257 1246 y(primijenimo)29 b(k)m(om)m(utacijsk)m(e)k(relacije)e (\(2.68\))h(za)g(op)s(eratore)g Fm(a)2608 1261 y Fi(n)2687 1246 y Ft(i)g Fm(a)2798 1210 y Fl(y)2798 1270 y Fi(n)2845 1246 y Ft(.)43 b(T)-8 b(o)33 b(nam)e(da)5 b(je)33 b(relaciju)257 1426 y(p)s(otpunosti:)809 1612 y Fj(X)848 1787 y Fi(n)946 1696 y Fm(f)994 1711 y Fi(n)1041 1696 y Ft(\()p Fm(')p Ft(\))p Fm(f)1240 1654 y Fl(\003)1229 1720 y Fi(n)1279 1696 y Ft(\()p Fm(')1381 1654 y Fl(0)1404 1696 y Ft(\))27 b(=)h Fp(\000)1660 1628 y Fm(\025)22 b Fp(\000)h Ft(1)p 1660 1672 228 4 v 1729 1764 a Fm(\032)1779 1779 y Fr(0)1898 1696 y Fm(@)1949 1711 y Fi(')1999 1696 y Fm(@)2050 1711 y Fi(')2096 1692 y Fe(0)2123 1696 y Fm(\016)t Ft(\()p Fm(')f Fp(\000)h Fm(')2458 1654 y Fl(0)2481 1696 y Ft(\))f(+)g Fm(\025@)2747 1711 y Fi(')2798 1696 y Ft(ctg)2939 1628 y Fm(')g Fp(\000)h Fm(')3189 1592 y Fl(0)p 2939 1672 273 4 v 3051 1764 a Ft(2)3222 1696 y Fm(:)302 b Ft(\(2.70\))257 1965 y(Nadalje,)38 b(uvrstimo)f(razv)m(o)5 b(j)38 b(\(2.67\))e(u)i (hamiltonijan)33 b(\(2.66\),)38 b(te)g(nametnimo)d(zah)m(tjev)j(dija-) 257 2145 y(gonalnosti)31 b(\(2.69\).)43 b(Nak)m(on)33 b(malo)d(algebre,)i(slijedi)1371 2347 y(1)p 1371 2391 49 4 v 1371 2483 a(2)1430 2414 y Fm(\032)1480 2429 y Fr(0)1536 2297 y Fj(Z)1636 2414 y Fm(d'f)1810 2373 y Fl(\003)1799 2439 y Fi(m)1865 2414 y Ft(\()p Fm(')p Ft(\))p Fm(f)2053 2429 y Fi(n)2100 2414 y Ft(\()p Fm(')p Ft(\))27 b(=)h Fm(!)2432 2429 y Fi(m)2498 2414 y Fm(\016)2541 2429 y Fi(n;m)2670 2414 y Fm(:)854 b Ft(\(2.71\))257 2683 y(P)m(omno)m(\024)-46 b(zimo)41 b(gornju)h(relaciju)f(s)i Fm(f)1607 2647 y Fl(\003)1596 2708 y Fi(m)1663 2683 y Ft(\()p Fm(')1765 2647 y Fl(0)1788 2683 y Ft(\))f(te)h(sumira)5 b(jmo)40 b(p)s(o)i Fm(m)p Ft(,)k(pa)c(uz)h(primjen)m(u)f(relacije)257 2864 y(p)s(otpunosti)32 b(\(2.70\),)g(k)m(ona)m(\024)-46 b(cno)34 b(dobiv)-5 b(amo)30 b(jednad)m(\024)-46 b(zbu)34 b(za)f(funk)m(ciju)g Fm(f)2894 2879 y Fi(n)2941 2864 y Ft(\()p Fm(')p Ft(\):)813 3133 y Fm(!)874 3148 y Fi(n)921 3133 y Fm(f)969 3148 y Fi(n)1016 3133 y Ft(\()p Fm(')p Ft(\))27 b(=)1297 3066 y Fm(\025)22 b Fp(\000)g Ft(1)p 1297 3110 228 4 v 1386 3201 a(2)1534 3133 y Fm(@)1590 3092 y Fr(2)1585 3158 y Fi(')1636 3133 y Fm(f)1684 3148 y Fi(n)1731 3133 y Ft(\()p Fm(')p Ft(\))g(+)2001 3066 y Fm(\025)p 2001 3110 57 4 v 2005 3201 a Ft(2)2068 3133 y Fm(\032)2118 3148 y Fr(0)2174 3016 y Fj(Z)2274 3133 y Fm(d')2389 3092 y Fl(0)2412 3133 y Fm(@)2463 3148 y Fi(')2509 3129 y Fe(0)2536 3133 y Ft(ctg)2677 3066 y Fm(')2741 3030 y Fl(0)2786 3066 y Fp(\000)h Fm(')p 2677 3110 273 4 v 2789 3201 a Ft(2)2960 3133 y Fm(f)3008 3148 y Fi(n)3055 3133 y Ft(\()p Fm(')3157 3092 y Fl(0)3180 3133 y Ft(\))p Fm(:)306 b Ft(\(2.72\))257 3402 y(Isk)m(oristimo)32 b(p)s(oznate)h(trigonometrijsk)m(e)e(relacije)973 3671 y Fm(@)1024 3686 y Fi(')1070 3667 y Fe(0)1097 3671 y Ft(ctg)1238 3604 y Fm(')1302 3568 y Fl(0)1347 3604 y Fp(\000)23 b Fm(')p 1238 3648 V 1350 3740 a Ft(2)1549 3671 y(=)k Fp(\000)1930 3604 y Ft(1)p 1739 3648 431 4 v 1739 3747 a(2)17 b(sin)1925 3708 y Fr(2)1991 3705 y Fi(')2037 3686 y Fe(0)2059 3705 y Fl(\000)p Fi(')p 1991 3724 170 4 v 2058 3782 a Fr(2)2207 3671 y Ft(=)28 b Fp(\000)2699 3604 y Ft(1)p 2398 3648 650 4 v 2398 3740 a(1)22 b Fp(\000)h Ft(cos)q(\()p Fm(')2802 3711 y Fl(0)2847 3740 y Fp(\000)g Fm(')p Ft(\))3058 3671 y Fm(;)466 b Ft(\(2.73\))257 3953 y(te)33 b(p)s(otra)m(\024)-46 b(zimo)31 b(rje)-5 b(\024)-44 b(senje)33 b(gornje)g(jednad)m(\024)-46 b(zb)s(e)33 b(u)g(obliku)e Fm(f)2373 3968 y Fi(n)2448 3953 y Fp(/)d Ft(exp)q(\()p Fp(\006)p Fm(in')p Ft(\).)45 b(Isk)m(oristimo)31 b(izraz)985 4105 y Fj(Z)1068 4132 y Fr(2)p Fi(\031)1031 4294 y Fr(0)1167 4222 y Fm(d')1319 4155 y Ft(exp)q(\()p Fp(\006)p Fm(in')p Ft(\))p 1319 4199 458 4 v 1357 4291 a(1)22 b Fp(\000)h Ft(cos)17 b Fm(')1814 4222 y Ft(=)1918 4105 y Fj(Z)2001 4132 y Fr(2)p Fi(\031)1964 4294 y Fr(0)2100 4222 y Fm(d')2281 4155 y Ft(cos)g Fm(n')p 2225 4199 382 4 v 2225 4291 a Ft(1)k Fp(\000)i Ft(cos)17 b Fm(')2644 4222 y Ft(=)27 b Fp(\000)p Ft(2)p Fm(\031)t Fp(j)p Fm(n)p Fp(j)p Fm(;)478 b Ft(\(2.74\))257 4492 y(te)29 b(uvrstimo)f(dobiv)m(eni)g(rezultat)g(u) h(jednad)m(\024)-46 b(zbu)30 b(\(2.72\))22 b(\024)-44 b(sto)29 b(nak)m(on)g(deriviranja)e(da)5 b(je)30 b(izraz)e(za)257 4672 y(disp)s(erzijsku)33 b(funk)m(ciju)g Fm(!)1227 4687 y Fi(n)1274 4672 y Ft(:)1350 4941 y Fm(!)1411 4956 y Fi(n)1485 4941 y Ft(=)1617 4874 y(1)p 1599 4918 87 4 v 1599 5010 a Fm(r)1646 4975 y Fr(2)1643 5031 y(0)1711 4795 y Fj( )1777 4941 y Fp(\000)1864 4874 y Fm(\025)23 b Fp(\000)f Ft(1)p 1864 4918 228 4 v 1954 5010 a(2)2102 4941 y Fm(n)2160 4900 y Fr(2)2222 4941 y Ft(+)2330 4874 y Fm(N)10 b(\025)p 2330 4918 146 4 v 2378 5010 a Ft(2)2485 4941 y Fp(j)p Fm(n)p Fp(j)2599 4795 y Fj(!)2681 4941 y Fm(:)843 b Ft(\(2.75\))257 5210 y(gdje)25 b(je)g Fm(r)600 5225 y Fr(0)664 5210 y Ft(radijus)f(kru)m(\024)-46 b(znice)25 b(na)g(k)m(o)5 b(jo)g(j)25 b(su)g(smje)-5 b(\024)-44 b(stene)23 b(\024)-46 b(cestice)26 b(u)e(mo)s(delu)g(\(vidi)f(nap)s (omen)m(u)h(iza)257 5391 y(izraza)k(za)g(hamiltonijan)d(\(2.22\)\),)j (a)g(za)h Fm(\032)1814 5406 y Fr(0)1882 5391 y Ft(smo)f(uvrstili)e (rezultat)i(dobiv)m(en)h(normalizacijom.)p eop %%Page: 20 23 20 22 bop 257 -89 a Fs(2.)44 b(CALOGER)m(O-SUTHERLANDO)m(V)33 b(MODEL)1489 b Ft(20)404 294 y(Na)31 b(kra)5 b(j)32 b(jo)-5 b(\024)-44 b(s)31 b(moramo)e(pro)m(vjeriti)i(nenegativnost)g(vlastitih) f(frekv)m(encija)i Fm(!)3264 309 y Fi(n)3311 294 y Ft(,)f(u)h(oba)f (mo-)257 474 y(dela.)41 b(Lak)m(o)27 b(se)g(mo)m(\024)-46 b(zemo)25 b(uvjeriti)g(da)h(su)h(oba)f(izraza)g(za)g(vlastite)g(frekv)m (encije)h(\(relacije)e(\(2.51\))257 655 y(i)37 b(\(2.75\)\))f(p)s (ozitivno)g(de\014nitne,)j(uk)m(olik)m(o)d(je)i Fm(\025)d(<)h Ft(1.)57 b(U)37 b(slu)m(\024)-46 b(ca)5 b(ju)38 b(k)-5 b(ada)37 b(je)g Fm(\025)f(>)f Ft(1,)j(dobijemo)257 835 y(uvjet)c(na)e(kv)-5 b(an)m(tni)33 b(bro)5 b(j)32 b Fm(n)h Ft(oblik)-5 b(a)1823 1016 y Fp(j)p Fm(n)p Fp(j)27 b Fm(<)g(a\032)2168 1031 y Fr(0)2208 1016 y Fm(;)1316 b Ft(\(2.76\))257 1251 y(gdje)33 b(je)g Fm(a)c Fp(\030)g Ft(1)j(p)s(ozitivna)g(k)m(onstan)m (ta.)45 b(U)33 b(na)-5 b(\024)-44 b(sem)33 b(pribli)m(\024)-46 b(zenju)31 b(ta)5 b(j)33 b(uvjet)h(je)f(uvijek)g(ispunjen)257 1431 y(jer)g(je)g Fm(\032)557 1446 y Fr(0)624 1431 y Fp(/)28 b Fm(N)10 b Ft(,)33 b(a)g(energija)e(p)s(obud)p 1557 1379 31 4 v(enja)i(mora)f(biti)f(mala.)p eop %%Page: 21 24 21 23 bop 257 1082 a Fv(P)-6 b(ogla)g(vlje)76 b(3)257 1622 y(Nerelativisti)-6 b(\024)-110 b(ck)-13 b(a,)75 b(samo)6 b(dualna)257 1996 y(Chern-Simonso)-6 b(v)-13 b(a)77 b(teorija)257 2508 y Ft(Chern-Simonso)m(v)-5 b(a)48 b(teorija)e(opisuje)i(nabijena)g(sk)-5 b(alarna)47 b(p)s(olja)f(u)i (\(2)32 b(+)h(1\)-dimenzijsk)m(om)257 2689 y(prostor-vremen)m(u,)28 b(minimalno)21 b(v)m(ezana)26 b(s)g(ba)m(\024)-46 b(zdarnim)24 b(p)s(oljem.)39 b(Dinamik)-5 b(a)22 b(ba)m(\024)-46 b(zdarnog)25 b(p)s(olja)257 2869 y(nije)32 b(opisana)g(uobi)m(\024)-46 b(ca)5 b(jenim)31 b(Maxw)m(ello)m(vim)e(\024)-46 b(clanom,)31 b(v)m(e)m(\023)-46 b(c)34 b(je)e(oblik)-5 b(a)1190 3137 y Fp(L)1259 3152 y Fi(C)5 b(hS)1432 3137 y Ft(=)28 b Fm(\017)1575 3152 y Fi(\026\027)t(\032)1697 3137 y Fm(T)14 b(r)1831 3016 y Fj(\022)1892 3137 y Fm(@)1948 3096 y Fi(\026)1996 3137 y Fm(A)2069 3096 y Fi(\027)2112 3137 y Fm(A)2185 3096 y Fi(\032)2248 3137 y Ft(+)2356 3070 y(2)p 2356 3114 49 4 v 2356 3205 a(3)2414 3137 y Fm(A)2487 3096 y Fi(\026)2534 3137 y Fm(A)2607 3096 y Fi(\027)2650 3137 y Fm(A)2723 3096 y Fi(\032)2764 3016 y Fj(\023)2841 3137 y Fm(:)732 b Ft(\(3.1\))257 3405 y(T)-8 b(a)37 b(mogu)m(\023)-46 b(cnost)35 b(opisiv)-5 b(anja)35 b(ba)m(\024)-46 b(zdarnih)35 b(p)s(olja)g(tzv.)55 b(Chern-Simonso)m(vim)32 b(\024)-46 b(clanom)34 b(k)-5 b(arakte-)257 3585 y(ristik)g(a)33 b(je)i(neparno-dimenzijsk)m(og)f(prostor-vremena.)50 b(P)m(osebno,)37 b(u)e(\(2)23 b(+)h(1\)-dimenzijsk)m(om)257 3766 y(prostor-vremen)m(u)47 b(deriv)-5 b(ativni)41 b(\024)-46 b(clan)45 b(je)h(kv)-5 b(adrati)m(\024)-46 b(can)45 b(u)h(p)s(oljima.) 80 b(Mogu)m(\023)-46 b(ce)46 b(je)g(u)g(Chern-)257 3946 y(Simonso)m(v)22 b(lagran)m(\024)-46 b(zijan)19 b(uklju)m(\024)-46 b(citi)20 b(i)h(Maxw)m(ello)m(v)e(\024)-46 b(clan,)23 b(no)f(k)-5 b(ak)m(o)22 b(je)g(on)g(kv)-5 b(adrati)m(\024)-46 b(can)21 b(u)h(deriv)-5 b(aci-)257 4127 y(jama,)36 b(mo)m(\024)-46 b(zemo)35 b(ga)g(zanemariti)f(na)i(v)m(elikim)e(udaljenostima,)g(tj.)54 b(niskim)34 b(enegijama.)52 b(Nas)255 4308 y(\023)-46 b(ce)38 b(zanimati)e(samo)h(Ab)s(elo)m(v)-5 b(a)38 b(teorija,)g(k)-5 b(ad)38 b(ba)m(\024)-46 b(zdarna)38 b(p)s(olja)f Fm(A)2702 4271 y Fi(\026)2787 4308 y Ft(med)p 2931 4255 31 4 v(usobno)h(k)m(om)m (utira)5 b(ju,)257 4488 y(te)44 b(u)g(tom)f(slu)m(\024)-46 b(ca)5 b(ju)44 b(drugi)d(\024)-46 b(clan)43 b(u)h(gornjem)f(izrazu)g (otpada.)77 b(T)-8 b(ak)m(o)s(d)p 2932 4436 V(er,)48 b(prou)m(\024)-46 b(ca)m(v)-5 b(at)41 b(\023)-46 b(cemo)257 4669 y(nerelativisti)m(\024)g(cki)31 b(limes)f(teorije.)404 4849 y(Kao)18 b(\024)-44 b(sto)25 b(smo)e(u)i(naslo)m(vu)f(nazna)m (\024)-46 b(cili,)24 b(jo)-5 b(\024)-44 b(s)21 b(\023)-46 b(cemo)24 b(dalje)f(ograni)m(\024)-46 b(citi)22 b(mogu)m(\023)-46 b(ce)23 b(Chern-Simons-)257 5030 y(o)m(v)m(e)38 b(teorije)e(na)h(samo)s (dualne.)55 b(T)-8 b(o)37 b(je)g(vrlo)f(bitno)f(o)s(dred)p 2386 4977 V(enje)j(teorije;)g(o)s(dnosi)e(se)i(na)e(teorije)257 5210 y(u)j(k)m(o)5 b(jima)36 b(je)i(med)p 932 5158 V(udjelo)m(v)-5 b(anje)38 b(p)s(osebnog)h(oblik)-5 b(a,)37 b(te)h(p)s(osebno)h (izabrane)e(jak)m(osti,)j(tak)m(o)e(da)257 5391 y(se)i(jednad)m(\024) -46 b(zb)s(e)40 b(gibanja,)g(k)m(o)5 b(je)40 b(su)g(op)m(\023)-46 b(cenito)38 b(v)m(ezane,)43 b(nelinearne)38 b(jednad)m(\024)-46 b(zb)s(e)41 b(drugog)d(reda,)1980 5674 y(21)p eop %%Page: 22 25 22 24 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(22)257 294 y(reducira)5 b(ju)41 b(na)g(jednad)m(\024)-46 b(zb)s(e)42 b(prv)m(og)f(reda,)d(\024)-44 b(sto)41 b(analizu)f(problema)c(\024)-46 b(cini)40 b(bitno)g(jednosta)m (vni-)257 474 y(jom.)47 b(Fizik)-5 b(alno)31 b(zna)m(\024)-46 b(cenje)35 b(takv)m(og)g(izb)s(ora)d(je)j(u)f(tome)28 b(\024)-44 b(sto)34 b("samo)s(dualna)e(to)m(\024)-46 b(ck)-5 b(a")34 b(o)s(dgo)m(v)-5 b(ara)257 655 y(minimalizaciji)26 b(nek)m(og)34 b(funk)m(cionala,)29 b(\024)-46 b(cesto)33 b(energije)f(ili)e(ak)m(cije.)257 1075 y Fk(3.1)161 b(Kolektivna)55 b(form)l(ulacija)g(mo)t(dela)257 1354 y Ft(Analizirat)39 b(\023)-46 b(cemo)44 b(sistem)g Fm(N)53 b Ft(\024)-46 b(cestica)44 b(b)s(ez)h(spina)f(k)m(o)5 b(je)46 b(su)f(smje)-5 b(\024)-44 b(stene)46 b(u)e(ra)m(vnini)g(i)d(\024)-46 b(cije)44 b(je)257 1535 y(med)p 401 1483 31 4 v(udjelo)m(v)-5 b(anje)36 b(dano)h(Chern-Simonso)m(vim)32 b(\024)-46 b(clanom.)53 b(Hamiltonijan)32 b(tog)k(sistema)g(je)h(dan)257 1716 y(izrazom)1401 1896 y Fm(H)f Ft(=)1656 1788 y Fi(N)1628 1813 y Fj(X)1621 1994 y Fi(n)p Fr(=1)1781 1829 y Ft(1)p 1781 1873 49 4 v 1781 1965 a(2)1839 1896 y(\()p Fp(\000)p Fm(i)p Fp(r)2071 1911 y Fi(n)2140 1896 y Ft(+)22 b Fu(A)2323 1911 y Fi(n)2370 1896 y Ft(\))2408 1855 y Fr(2)2469 1896 y Ft(+)g Fm(V)5 b(;)944 b Ft(\(3.2\))257 2120 y(gdje)33 b(je)g Fu(A)657 2135 y Fi(n)736 2120 y Ft(statisti)m(\024)-46 b(ck)m(o)32 b(ba)m(\024)-46 b(zdarno)33 b(p)s(olje)1224 2383 y Fm(A)1297 2342 y Fi(i)1297 2408 y(n)1372 2383 y Ft(=)27 b Fp(j)p Fm(\025)p Fp(j)p Fm(\017)1627 2342 y Fi(ij)1753 2275 y(N)1724 2300 y Fj(X)1704 2485 y Fi(m)p Fl(6)p Fr(=)p Fi(n)1891 2316 y Ft(\()p Fu(r)1975 2331 y Fi(n)2044 2316 y Fp(\000)22 b Fu(r)2189 2331 y Fi(m)2256 2316 y Ft(\))2294 2280 y Fi(j)p 1891 2360 440 4 v 1900 2452 a Fp(j)p Fu(r)1974 2467 y Fi(n)2042 2452 y Fp(\000)h Fu(r)2188 2467 y Fi(m)2254 2452 y Fp(j)2282 2423 y Fr(2)2340 2383 y Fm(;)44 b(i;)17 b(j)34 b Ft(=)28 b(1)p Fm(;)17 b Ft(2)p Fm(;)765 b Ft(\(3.3\))257 2658 y(a)40 b(sk)-5 b(alarni)39 b(p)s(otencijal)g Fm(V)62 b Ft(o)s(dredit)36 b(\023)-46 b(cemo)40 b(k)-5 b(asnije.)67 b(Na)40 b(tren)m(utak)e(\023) -46 b(cemo)40 b(promijeniti)d(v)-5 b(ari-)257 2838 y(jable;)41 b(v)m(ektor)f Fu(r)882 2853 y Fi(n)928 2838 y Ft(,)g(k)m(o)5 b(ji)39 b(ozna)m(\024)-46 b(ca)m(v)-5 b(a)38 b(p)s(olo)m(\024)-46 b(za)5 b(j)38 b(n-tog)f(b)s(ozona)h(zamijenit)c(\023)-46 b(cemo)38 b(k)m(ompleksnim)257 3019 y(v)-5 b(arijablama)29 b Fm(z)833 3034 y Fi(n)913 3019 y Ft(i)38 b(\026)-55 b Fm(z)1018 3034 y Fi(n)1065 3019 y Ft(:)1179 3273 y Fm(z)32 b Fp(\021)d Fm(x)22 b Ft(+)g Fm(iy)t(;)50 b Ft(\026)-55 b Fm(z)32 b Fp(\021)d Fm(x)22 b Fp(\000)h Fm(iy)1214 3412 y(@)p 1189 3456 107 4 v 1189 3547 a(@)5 b(z)1333 3479 y Ft(=)1447 3412 y(1)p 1447 3456 49 4 v 1447 3547 a(2)1522 3333 y Fj( )1626 3412 y Fm(@)p 1598 3456 113 4 v 1598 3547 a(@)g(x)1742 3479 y Fp(\000)23 b Fm(i)1911 3412 y(@)p 1885 3456 109 4 v 1885 3547 a(@)5 b(y)2003 3333 y Fj(!)2085 3479 y Fm(;)2192 3412 y(@)p 2167 3456 107 4 v 2167 3547 a(@)11 b Ft(\026)-55 b Fm(z)2311 3479 y Ft(=)2425 3412 y(1)p 2425 3456 49 4 v 2425 3547 a(2)2500 3333 y Fj( )2603 3412 y Fm(@)p 2576 3456 113 4 v 2576 3547 a(@)5 b(x)2720 3479 y Ft(+)22 b Fm(i)2887 3412 y(@)p 2861 3456 109 4 v 2861 3547 a(@)5 b(y)2979 3333 y Fj(!)3600 3479 y Ft(\(3.4\))257 3734 y(U)33 b(tim)e(no)m(vim)h(v)-5 b(arijablam)29 b(hamiltonijan)g(\(3.2\))j(je)g(dan)h(izrazom:)696 4032 y Fm(H)i Ft(=)48 b Fp(\000)1065 3924 y Fi(N)1037 3949 y Fj(X)1030 4130 y Fi(n)p Fr(=1)1291 3965 y Fm(@)1347 3928 y Fr(2)p 1190 4009 299 4 v 1190 4100 a Fm(@)5 b(z)1291 4115 y Fi(n)1339 4100 y Fm(@)11 b Ft(\026)-55 b Fm(z)1440 4115 y Fi(n)1520 4032 y Fp(\000)1655 3924 y Fi(N)1626 3949 y Fj(X)1620 4130 y Fi(n)p Fr(=1)1881 3965 y Fm(@)1937 3928 y Fr(2)p 1779 4009 V 1779 4100 a Fm(@)11 b Ft(\026)-55 b Fm(z)1880 4115 y Fi(n)1929 4100 y Fm(@)5 b(z)2030 4115 y Fi(n)2110 4032 y Ft(+)2218 3965 y Fp(j)p Fm(\025)p Fp(j)2331 3928 y Fr(2)p 2218 4009 152 4 v 2269 4100 a Ft(2)2431 3924 y Fi(N)2403 3949 y Fj(X)2396 4130 y Fi(n)p Fr(=1)2546 3858 y Fj(\014)2546 3907 y(\014)2546 3957 y(\014)2546 4007 y(\014)2546 4057 y(\014)2546 4107 y(\014)2622 3924 y Fi(N)2594 3949 y Fj(X)2573 4133 y Fi(n)p Fl(6)p Fr(=)p Fi(m)2899 3965 y Ft(1)p 2760 4009 326 4 v 2760 4100 a Fm(z)2805 4115 y Fi(n)2875 4100 y Fp(\000)22 b Fm(z)3019 4115 y Fi(m)3096 3858 y Fj(\014)3096 3907 y(\014)3096 3957 y(\014)3096 4007 y(\014)3096 4057 y(\014)3096 4107 y(\014)3124 3884 y Fr(2)3185 4032 y Ft(+)g Fm(V)936 4351 y Fp(\000j)p Fm(\025)p Fp(j)1191 4243 y Fi(N)1163 4268 y Fj(X)1142 4453 y Fi(n)p Fl(6)p Fr(=)p Fi(m)1468 4284 y Ft(1)p 1329 4328 V 1335 4420 a(\026)-55 b Fm(z)1374 4435 y Fi(n)1444 4420 y Fp(\000)28 b Ft(\026)-55 b Fm(z)1588 4435 y Fi(m)1721 4284 y Fm(@)p 1675 4328 150 4 v 1675 4420 a(@)5 b(z)1776 4435 y Fi(n)1856 4351 y Ft(+)22 b Fp(j)p Fm(\025)p Fp(j)2132 4243 y Fi(N)2103 4268 y Fj(X)2083 4453 y Fi(n)p Fl(6)p Fr(=)p Fi(m)2408 4284 y Ft(1)p 2270 4328 326 4 v 2270 4420 a Fm(z)2315 4435 y Fi(n)2384 4420 y Fp(\000)h Fm(z)2529 4435 y Fi(m)2662 4284 y Fm(@)p 2616 4328 150 4 v 2616 4420 a(@)11 b Ft(\026)-55 b Fm(z)2717 4435 y Fi(n)2775 4351 y Fm(:)798 b Ft(\(3.5\))257 4626 y(T)-8 b(reba)33 b(uo)m(\024)-46 b(citi)30 b(nek)m(om)m(utativnost)j (parcijalnih)c(deriv)-5 b(acija)30 b(p)s(o)i Fm(z)37 b Ft(i)g(\026)-55 b Fm(z)5 b Ft(.)43 b(T)-8 b(o)32 b(je)g(p)s (osljedica)f(netri-)257 4806 y(vijalne)h(relacije:)1724 4919 y Fm(@)p 1699 4964 107 4 v 1699 5055 a(@)5 b(z)1826 4919 y Ft(1)p 1825 4964 50 4 v 1831 5055 a(\026)-55 b Fm(z)1913 4987 y Ft(=)27 b Fm(\031)t(\016)2122 4946 y Fr(\(2\))2216 4987 y Ft(\()p Fm(z)t Ft(\))p Fm(:)1232 b Ft(\(3.6\))257 5210 y(Prije)39 b(prijelaza)f(na)i(k)m(olektivne)g(v) -5 b(arijable,)39 b(jo)-5 b(\024)-44 b(s)37 b(\023)-46 b(cemo)39 b(transformirati)d(hamiltonijan)g(\(3.5\).)257 5391 y(Naime,)g(zanimat)c(\023)-46 b(ce)36 b(nas)h(v)m(orteksna)h(rje) -5 b(\024)-44 b(senja,)37 b(pa)f(iz)g(v)-5 b(alne)35 b(funk)m(cije)i(izvla)m(\024)-46 b(cimo)33 b(prefaktor)p eop %%Page: 23 26 23 25 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(23)257 227 y Fj(Q)336 314 y Fi(n;\013)448 294 y Ft(\()6 b(\026)-55 b Fm(z)531 309 y Fi(n)605 294 y Fp(\000)730 269 y Ft(\026)709 294 y Fm(Z)776 309 y Fi(\013)825 294 y Ft(\))863 258 y Fi(v)904 294 y Ft(,)41 b(gdje)f(je)f Fm(Z)1367 309 y Fi(\013)1456 294 y Ft(k)m(ompleksni)g(bro)5 b(j)39 b(k)m(o)5 b(ji)39 b(o)s(dred)p 2590 241 31 4 v(uje)h(p)s(olo)m(\024)-46 b(za)5 b(j)38 b(v)m(orteksa.)66 b(T)-8 b(ada)257 474 y(dobiv)j(amo)31 b(u)m(\024)-46 b(cink)m(o)m(vni)33 b(hamiltonijan)1735 449 y(~)1710 474 y Fm(H)812 678 y Ft(~)787 704 y Fm(H)i Ft(=)1028 621 y Fj(Y)1027 795 y Fi(n;\013)1135 704 y Ft(\()6 b(\026)-55 b Fm(z)1218 719 y Fi(n)1287 704 y Fp(\000)1408 678 y Ft(\026)1387 704 y Fm(Z)1454 719 y Fi(\013)1503 704 y Ft(\))1541 662 y Fl(\000)p Fi(v)1637 704 y Fm(H)1743 621 y Fj(Y)1742 795 y Fi(n;\013)1850 704 y Ft(\()6 b(\026)-55 b Fm(z)1933 719 y Fi(n)2002 704 y Fp(\000)2122 678 y Ft(\026)2102 704 y Fm(Z)2169 719 y Fi(\013)2218 704 y Ft(\))2256 662 y Fi(v)903 1040 y Ft(=)48 b Fp(\000)1156 932 y Fi(N)1128 957 y Fj(X)1121 1138 y Fi(n)p Fr(=1)1382 973 y Fm(@)1438 937 y Fr(2)p 1281 1017 299 4 v 1281 1108 a Fm(@)5 b(z)1382 1123 y Fi(n)1430 1108 y Fm(@)11 b Ft(\026)-55 b Fm(z)1531 1123 y Fi(n)1611 1040 y Fp(\000)1746 932 y Fi(N)1718 957 y Fj(X)1711 1138 y Fi(n)p Fr(=1)1972 973 y Fm(@)2028 937 y Fr(2)p 1871 1017 V 1871 1108 a Fm(@)11 b Ft(\026)-55 b Fm(z)1972 1123 y Fi(n)2020 1108 y Fm(@)5 b(z)2121 1123 y Fi(n)2201 1040 y Ft(+)2309 973 y Fp(j)p Fm(\025)p Fp(j)2422 937 y Fr(2)p 2309 1017 152 4 v 2360 1108 a Ft(2)2522 932 y Fi(N)2494 957 y Fj(X)2487 1138 y Fi(n)p Fr(=1)2637 866 y Fj(\014)2637 916 y(\014)2637 965 y(\014)2637 1015 y(\014)2637 1065 y(\014)2637 1115 y(\014)2713 932 y Fi(N)2685 957 y Fj(X)2665 1142 y Fi(n)p Fl(6)p Fr(=)p Fi(m)2990 973 y Ft(1)p 2851 1017 326 4 v 2851 1108 a Fm(z)2896 1123 y Fi(n)2966 1108 y Fp(\000)22 b Fm(z)3110 1123 y Fi(m)3187 866 y Fj(\014)3187 916 y(\014)3187 965 y(\014)3187 1015 y(\014)3187 1065 y(\014)3187 1115 y(\014)3215 892 y Fr(2)902 1359 y Fp(\000)48 b(j)p Fm(\025)p Fp(j)1205 1252 y Fi(N)1176 1276 y Fj(X)1156 1461 y Fi(n)p Fl(6)p Fr(=)p Fi(m)1481 1292 y Ft(1)p 1343 1336 V 1349 1428 a(\026)-55 b Fm(z)1388 1443 y Fi(n)1457 1428 y Fp(\000)29 b Ft(\026)-55 b Fm(z)1602 1443 y Fi(m)1735 1292 y Fm(@)p 1689 1336 150 4 v 1689 1428 a(@)5 b(z)1790 1443 y Fi(n)1870 1359 y Ft(+)22 b Fp(j)p Fm(\025)p Fp(j)2145 1252 y Fi(N)2117 1276 y Fj(X)2097 1461 y Fi(n)p Fl(6)p Fr(=)p Fi(m)2422 1292 y Ft(1)p 2283 1336 326 4 v 2283 1428 a Fm(z)2328 1443 y Fi(n)2398 1428 y Fp(\000)h Fm(z)2543 1443 y Fi(m)2675 1292 y Fm(@)p 2629 1336 150 4 v 2629 1428 a(@)11 b Ft(\026)-55 b Fm(z)2730 1443 y Fi(n)903 1677 y Ft(+)48 b Fp(j)p Fm(\025)p Fp(j)p Fm(v)1288 1569 y Fi(N)1259 1594 y Fj(X)1207 1778 y Fi(n)p Fl(6)p Fr(=)p Fi(m;\013)1597 1610 y Ft(1)p 1458 1654 326 4 v 1458 1745 a Fm(z)1503 1760 y Fi(n)1573 1745 y Fp(\000)22 b Fm(z)1717 1760 y Fi(m)1945 1610 y Ft(1)p 1804 1654 331 4 v 1810 1745 a(\026)-55 b Fm(z)1849 1760 y Fi(n)1919 1745 y Fp(\000)2039 1720 y Ft(\026)2018 1745 y Fm(Z)2085 1760 y Fi(\013)2167 1677 y Fp(\000)22 b Ft(2)p Fm(v)2411 1569 y Fi(N)2382 1594 y Fj(X)2389 1768 y Fi(n;\013)2670 1610 y Ft(1)p 2529 1654 V 2535 1745 a(\026)-55 b Fm(z)2574 1760 y Fi(n)2643 1745 y Fp(\000)2764 1720 y Ft(\026)2743 1745 y Fm(Z)2810 1760 y Fi(\013)2925 1610 y Fm(@)p 2879 1654 150 4 v 2879 1745 a(@)5 b(z)2980 1760 y Fi(n)3060 1677 y Ft(+)22 b Fm(V)5 b(:)353 b Ft(\(3.7\))257 1926 y(Prelazimo)31 b(na)h(k)m(olektivne)h(v)-5 b(arijable)1536 2164 y Fm(\032)p Ft(\()p Fu(r)p Ft(\))48 b(=)1895 2056 y Fi(N)1866 2081 y Fj(X)1860 2262 y Fi(n)p Fr(=1)2009 2164 y Fm(\016)2056 2123 y Fr(\(2\))2151 2164 y Ft(\()p Fu(r)21 b Fp(\000)i Fu(r)2402 2123 y Fl(0)2402 2188 y Fi(n)2449 2164 y 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3750 y Ft(=)1806 3633 y Fj(Z)1906 3750 y Fm(d)1957 3709 y Fr(2)1996 3750 y Fu(r)2052 3683 y Fm(@)g(\032)p Ft(\()p Fu(r)p Ft(\))p 2052 3727 229 4 v 2091 3818 a Fm(@)g(z)2192 3833 y Fi(n)2386 3683 y Fm(\016)p 2300 3727 219 4 v 2300 3818 a(\016)t(\032)p Ft(\()p Fu(r)p Ft(\))2529 3750 y Fm(;)1541 3951 y(@)p 1495 3995 150 4 v 1495 4087 a(@)11 b Ft(\026)-55 b Fm(z)1596 4102 y Fi(n)1702 4019 y Ft(=)1806 3902 y Fj(Z)1906 4019 y Fm(d)1957 3978 y Fr(2)1996 4019 y Fu(r)2052 3951 y Fm(@)5 b(\032)p Ft(\()p Fu(r)p Ft(\))p 2052 3995 229 4 v 2091 4087 a Fm(@)11 b Ft(\026)-55 b Fm(z)2192 4102 y Fi(n)2386 3951 y Fm(\016)p 2300 3995 219 4 v 2300 4087 a(\016)t(\032)p Ft(\()p Fu(r)p Ft(\))2529 4019 y Fm(:)995 b Ft(\(3.11\))257 4248 y(Nak)m(on)34 b(malo)c(ra)m(\024)-46 b(cuna)33 b(dobiv)-5 b(amo)470 4477 y Fm(H)35 b Ft(=)700 4410 y(1)p 700 4454 49 4 v 700 4545 a(2)775 4360 y Fj(Z)875 4477 y Fm(d)926 4436 y Fr(2)965 4477 y Fu(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\)\()p Fp(r)p Fm(\031)t Ft(\()p Fu(r)p Ft(\)\))1523 4436 y Fr(2)1583 4477 y Ft(+)1691 4410 y(1)p 1691 4454 V 1691 4545 a(2)1767 4360 y Fj(Z)1866 4477 y Fm(d)1917 4436 y Fr(2)1957 4477 y Fu(r)p Fm(!)t Ft(\()p Fu(r)p Ft(\))2284 4410 y Fm(\016)p 2200 4454 219 4 v 2200 4545 a(\016)t(\032)p Ft(\()p Fu(r)p Ft(\))470 4766 y Fp(\000)p Fm(\025v)672 4649 y Fj(Z)771 4766 y Fm(d)822 4725 y Fr(2)861 4766 y Fu(r)p Fm(d)958 4725 y Fr(2)997 4766 y Fu(r)1043 4725 y Fl(0)1076 4699 y Ft(\()p Fu(r)22 b Fp(\000)h Fu(r)1328 4663 y Fl(0)1351 4699 y Ft(\)\()p Fu(r)f Fp(\000)g Fu(r)1640 4663 y Fl(00)1682 4699 y Ft(\))h Fp(\000)f Fm(i)1878 4673 y Ft(^)1875 4699 y Fm(k)t Ft(\()p Fu(r)f Fp(\000)i Fu(r)2181 4663 y Fl(0)2204 4699 y Ft(\))f Fp(\002)h Ft(\()p Fu(r)f Fp(\000)g Fu(r)2615 4663 y Fl(00)2657 4699 y Ft(\))p 1076 4743 1620 4 v 1545 4835 a Fp(j)p Fu(r)f Fp(\000)i Fu(r)1786 4806 y Fl(0)1809 4835 y Fp(j)1837 4806 y Fr(2)1876 4835 y Fp(j)p Fu(r)f Fp(\000)g Fu(r)2117 4806 y Fl(00)2160 4835 y Fp(j)2188 4806 y Fr(2)2705 4766 y Fm(\032)p Ft(\()p Fu(r)p Ft(\))p 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5315 y(^)1053 5341 y Fm(k)j Fp(\002)1229 5195 y Fj( )1294 5341 y Fp(\000)p Fm(\025)1445 5224 y Fj(Z)1545 5341 y Fm(d)1596 5300 y Fr(2)1635 5341 y Fu(r)1681 5300 y Fl(0)1704 5341 y Fm(\032)p Ft(\()p Fu(r)1838 5300 y Fl(0)1862 5341 y Ft(\))1957 5274 y Fu(r)d Fp(\000)g Fu(r)2170 5238 y Fl(0)p 1910 5318 332 4 v 1910 5409 a Fp(j)p Fu(r)f Fp(\000)i Fu(r)2151 5381 y Fl(0)2174 5409 y Fp(j)2202 5381 y Fr(2)2273 5341 y Ft(+)f Fm(v)2438 5224 y Fj(Z)2538 5341 y Fm(d)2589 5300 y Fr(2)2628 5341 y Fu(r)2674 5300 y Fl(0)2697 5341 y Fm(n)p Ft(\()p Fu(r)2839 5300 y Fl(0)2862 5341 y Ft(\))2958 5274 y Fu(r)g Fp(\000)g Fu(r)3171 5238 y Fl(0)p 2910 5318 V 2910 5409 a Fp(j)p Fu(r)g Fp(\000)g Fu(r)3151 5381 y Fl(0)3175 5409 y Fp(j)3203 5381 y Fr(2)3252 5195 y Fj(!)3334 5341 y Fm(\031)t Ft(\()p Fu(r)p Ft(\))p Fm(;)9 b Ft(\(3.12\))p eop %%Page: 24 27 24 26 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(24)257 294 y(gdje)33 b(smo)f(uv)m(eli)g (gusto)m(\023)-46 b(cu)33 b(v)m(orteksa)h Fm(n)p Ft(\()p Fu(r)p Ft(\))1533 535 y Fm(n)p Ft(\()p Fu(r)p Ft(\))27 b(=)1844 452 y Fj(X)1881 627 y Fi(\013)1980 535 y Fm(\016)2027 494 y Fr(\(2\))2122 535 y Ft(\()p Fu(r)22 b Fp(\000)g Fu(R)2411 550 y Fi(\013)2460 535 y Ft(\))p Fm(;)1026 b Ft(\(3.13\))257 777 y(te)33 b(p)s(okratu)g Fm(!)t Ft(\()p Fu(r)p Ft(\))957 1019 y Fm(!)t Ft(\()p Fu(r)p Ft(\))27 b(=)g Fp(\000)p Ft(\001)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))c(+)f(2)p Fm(v)t Fp(r)1925 872 y Fj( )1990 1019 y Fm(\032)p Ft(\()p Fu(r)p Ft(\))2179 901 y Fj(Z)2278 1019 y Fm(d)2329 977 y Fr(2)2368 1019 y Fu(r)2414 977 y Fl(0)2437 1019 y Fm(n)p Ft(\()p Fu(r)2579 977 y Fl(0)2602 1019 y Ft(\))2698 951 y Fu(r)g Fp(\000)g Fu(r)2911 915 y Fl(0)p 2650 995 332 4 v 2650 1087 a Fp(j)p Fu(r)g Fp(\000)h Fu(r)2892 1058 y Fl(0)2915 1087 y Fp(j)2943 1058 y Fr(2)2992 872 y Fj(!)3074 1019 y Fm(:)450 b Ft(\(3.14\))257 1283 y(V)-8 b(ektor)573 1257 y(^)570 1283 y Fm(k)31 b Ft(je)e(jedini)m(\024)-46 b(cni)27 b(v)m(ektor)i(ok)m(omit)e(na)h(ra)m(vnin)m(u)h(u)g(k)m(o)5 b(jo)g(j)29 b(je)f(de\014niran)g(problem.)41 b(Vidimo)257 1464 y(da)28 b(hamiltonijan)d(\(3.12\))i(nije)g(hermitski,)h(i)f(to)h (zb)s(og)d(\024)-46 b(clana)27 b(k)m(o)5 b(ji)28 b(sadr)m(\024)-46 b(zi)28 b Fm(!)t Ft(\()p Fu(r)p Ft(\).)41 b(Sli)m(\024)-46 b(cno)27 b(k)-5 b(ao)27 b(i)g(u)257 1644 y(pretho)s(dnom)35 b(p)s(ogla)m(vlju,)e(resk)-5 b(aliramo)33 b(v)-5 b(alni)33 b(funk)m(cional)h(k)m(oriste)m(\023)-46 b(ci)34 b(jak)m(obijan)g (transforma-)257 1825 y(cije,)j(te)f(transformiramo)d(sam)j (hamiltonijan)c(i)j(k)m(ona)m(\024)-46 b(cno)37 b(imamo)d(hermitski)g (hamiltonijan)257 2005 y(Chern-Simonso)m(v)m(e)g(teorije)e(u)g(form)m (ulaciji)d(k)m(olektivne)k(teorije)f(p)s(olja:)305 2260 y Fm(H)j Ft(=)535 2193 y(1)p 535 2237 49 4 v 535 2328 a(2)610 2143 y Fj(Z)710 2260 y Fm(d)761 2219 y Fr(2)800 2260 y Fu(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))1035 2114 y Fj(\()1101 2260 y Fp(r)p Fm(\031)t Ft(\()p Fu(r)p Ft(\))22 b Fp(\000)1489 2234 y Ft(^)1487 2260 y Fm(k)j Fp(\002)1663 2114 y Fj(")1711 2260 y Fp(\000)1798 2193 y Ft(1)p 1798 2237 V 1798 2328 a(2)1867 2193 y Fp(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))p 1867 2237 255 4 v 1909 2328 a Fm(\032)p Ft(\()p Fu(r)p Ft(\))2154 2260 y(+)2252 2143 y Fj(Z)2352 2260 y Fm(d)2403 2219 y Fr(2)2442 2260 y Fu(r)2488 2219 y Fl(0)2568 2193 y Fu(r)d Fp(\000)h Fu(r)2782 2156 y Fl(0)p 2521 2237 332 4 v 2521 2328 a Fp(j)p Fu(r)f Fp(\000)g Fu(r)2762 2300 y Fl(0)2785 2328 y Fp(j)2813 2300 y Fr(2)2862 2260 y Ft(\()p Fp(\000)p Fm(\025\032)p Ft(\()p Fu(r)3168 2219 y Fl(0)3192 2260 y Ft(\))g(+)g Fm(v)t(n)p Ft(\()p Fu(r)3543 2219 y Fl(0)3566 2260 y Ft(\)\))3642 2114 y Fj(#\))3757 2137 y Fr(2)305 2542 y Fp(\000)392 2475 y Ft(1)p 392 2519 49 4 v 392 2611 a(4)468 2425 y Fj(Z)568 2542 y Fm(d)619 2501 y Fr(2)658 2542 y Fu(r)714 2475 y Fm(\016)t(!)t Ft(\()p Fu(r)p Ft(\))p 714 2519 233 4 v 721 2611 a Fm(\016)t(\032)p Ft(\()p Fu(r)p Ft(\))979 2542 y(+)g Fm(\031)1152 2425 y Fj(Z)1252 2542 y Fm(d)1303 2501 y Fr(2)1342 2542 y Fu(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))1577 2396 y Fj(")1625 2542 y Fm(\025\032)p Ft(\()p Fu(r)p Ft(\))g(+)1984 2475 y Fm(\025v)p 1984 2519 108 4 v 2013 2611 a Ft(2)2101 2542 y Fm(n)p Ft(\()p Fu(r)p Ft(\))2281 2396 y Fj(#)2352 2542 y Ft(+)g Fm(V)5 b(:)1025 b Ft(\(3.15\))257 2784 y(Drugi)37 b(\024)-46 b(clan)40 b(u)h(hamiltonijan)m(u)d(\(3.15\))i(je)h(singularan,)g(no)g(ne)h (doprinosi)d(u)i(v)m(o)s(de)m(\023)-46 b(cem)42 b(redu)257 2964 y(u)35 b Fm(N)10 b Ft(.)51 b(Kasnije)32 b(\023)-46 b(cemo)34 b(p)s(ok)-5 b(azati)34 b(da)h(se)h(ta)5 b(j)32 b(\024)-46 b(clan)34 b(krati)g(s)h(b)s(esk)m(ona)m(\024)-46 b(cnim)35 b(doprinosom)f(n)m(ultih)257 3145 y(oscilacija)23 b(u)h(kv)-5 b(an)m(tnom)25 b(sp)s(ektru)h(\015uktuacija)e(ok)m(o)h(k)m (olektivnog)g(p)s(olja)d Fm(\032)p Ft(\()p Fu(r)p Ft(\).)41 b(U)25 b(tre)m(\023)-46 b(cem)22 b(\024)-46 b(clan)m(u)257 3326 y(mo)m(\024)g(zemo)36 b(zab)s(ora)m(viti)g Fm(\025v)41 b Ft(doprinos,)d(jer)f(su)h(gusto)m(\023)-46 b(ce)38 b Fm(\032)p 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Fm(\025\031)t(N)10 b(\016)t Ft(\(0\))p Fm(;)257 4673 y Ft(dobiv)-5 b(amo)33 b(Jac)m(kiw-Pi)i(mo)s(del,)f(tj.)51 b(samo)s(dualn)m(u)34 b(Chern-Simonso)m(vu)h(teoriju)f(u)h(form)m (ulaciji)257 4853 y(k)m(olektivne)e(teorije)f(p)s(olja)264 5108 y Fm(H)j Ft(=)514 5041 y(1)p 514 5085 49 4 v 514 5176 a(2)589 4991 y Fj(Z)689 5108 y Fm(d)740 5067 y Fr(2)779 5108 y Fu(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))1014 4962 y Fj(")1062 5108 y Fp(r)p Fm(\031)t Ft(\()p Fu(r)p Ft(\))22 b(+)1448 5082 y(^)1446 5108 y Fm(k)j Fp(\002)1622 4962 y Fj( )1697 5041 y Ft(1)p 1697 5085 V 1697 5176 a(2)1766 5041 y Fp(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))p 1766 5085 255 4 v 1807 5176 a Fm(\032)p Ft(\()p Fu(r)p Ft(\))2053 5108 y(+)d Fp(j)p Fm(\025)p Fp(j)2281 4991 y Fj(Z)2380 5108 y Fm(d)2431 5067 y Fr(2)2470 5108 y Fu(r)2516 5067 y Fl(0)2539 5108 y Fm(\032)p Ft(\()p Fu(r)2673 5067 y Fl(0)2696 5108 y Ft(\))2791 5041 y Fu(r)g Fp(\000)h Fu(r)3005 5004 y Fl(0)p 2744 5085 332 4 v 2744 5176 a Fp(j)p Fu(r)f Fp(\000)g Fu(r)2985 5148 y Fl(0)3008 5176 y Fp(j)3036 5148 y Fr(2)3107 5108 y Fp(\000)h Fm(v)3315 5041 y Fu(r)f Fp(\000)h Fu(R)p 3268 5085 346 4 v 3268 5176 a Fp(j)p Fu(r)e Fp(\000)i Fu(R)p Fp(j)3575 5148 y Fr(2)3624 4962 y Fj(!)o(#)3738 4985 y Fr(2)504 5372 y Ft(+)590 5305 y(1)p 590 5349 49 4 v 590 5441 a(4)665 5255 y Fj(Z)765 5372 y Fm(d)816 5331 y Fr(2)855 5372 y Fu(r)p Ft(\001)p Fm(\016)1029 5331 y Fr(\(2\))1123 5372 y Ft(\()p Fu(r)f Fp(\000)h Fu(r)1375 5331 y Fl(0)1398 5372 y Ft(\))p Fp(j)1464 5387 y Fd(r)p Fr(=)p Fd(r)1587 5368 y Fe(0)1634 5372 y Ft(+)f Fm(\025\031)t(N)10 b(\016)t Ft(\(0\))p Fm(:)1416 b Ft(\(3.16\))p eop %%Page: 25 28 25 27 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(25)257 294 y(V)-8 b(e)m(\023)-46 b(c)48 b(smo)f(naglasili)d(v)-5 b(a)m(\024)-46 b(znost)47 b(samo)s(dualnog)e(limesa)h(teorije,)k(i)c(\014zik)-5 b(alno)46 b(zna)m(\024)-46 b(cenje)49 b(istog,)257 474 y(no)c(u)g(slu)m(\024)-46 b(ca)5 b(ju)46 b(Chern-Simonso)m(v)m(e)f (teorije,)j(p)s(osto)5 b(ji)44 b(i)g(b)s(on)m(us.)82 b(Naime,)46 b(p)s(ok)-5 b(azano)45 b(je)g([21])257 655 y(da)f(je)f(samo)g(u)g(samo)s(dualnom)e(limesu)h(Chern-Simonso)m(v)-5 b(a)43 b(teorija)f(renormalizabilna,)g(tj.)257 835 y(ultraljubi)m(\024) -46 b(casto)46 b(k)m(ona)m(\024)-46 b(cna)49 b(u)g(svim)e(redo)m(vima)h (ra)m(\024)-46 b(cuna)48 b(smetnje.)91 b(U)49 b(sljede)m(\023)-46 b(cem)48 b(o)s(djeljku)255 1016 y(\023)-46 b(cemo)25 b(zanemariti)e(p)s(osljednja)i(dv)-5 b(a)26 b(singularna)c(\024)-46 b(clana)24 b(u)i(hamiltonijan)m(u)c(\(3.16\),)27 b(no)e(prilik)m(om)257 1197 y(razmatranja)31 b(kv)-5 b(an)m(tnih)33 b(\015uktucija)g(vidjet)c (\023)-46 b(cemo)32 b(da)h(za)g(to)f(p)s(osto)5 b(ji)31 b(opra)m(vdanje.)257 1621 y Fk(3.2)161 b(Bogomol'n)l(yijev)53 b(limes)257 1900 y Ft(Analizu)22 b(mo)s(dela)f(danog)h(hamilonijanom)c (\(3.16\))k(zap)s(o)m(\024)-46 b(cinjemo)21 b(u)i(klasi)m(\024)-46 b(cnom)21 b(pribli)m(\024)-46 b(zenju.)39 b(U)257 2080 y(teoriji)29 b(k)m(olektivnog)h(p)s(olja)f(to)h(zna)m(\024)-46 b(ci)30 b(da)e(\023)-46 b(cemo)30 b(razmotriti)25 b(\024)-46 b(clano)m(v)m(e)31 b(v)m(o)s(de)m(\023)-46 b(ce)32 b(u)e(1)p Fm(=)-5 b(N)41 b Ft(razv)m(o)5 b(ju.)257 2261 y(U)48 b(k)m(onkretnom)h(slu)m(\024)-46 b(ca)5 b(ju,)51 b(v)m(o)s(de)m(\023) -46 b(ci)48 b(dio)f(hamiltonijana)d(\(3.16\))j(je)g(dan)h(tzv.)90 b(u)m(\024)-46 b(cink)m(o)m(vnim)257 2441 y(p)s(otencijalom)413 2734 y Fm(V)470 2749 y Fr(u)n(\024)-33 b(c)q(in)631 2734 y Ft(=)745 2666 y(1)p 745 2710 49 4 v 745 2802 a(2)820 2616 y Fj(Z)920 2734 y Fm(d)971 2692 y Fr(2)1010 2734 y Fu(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))1245 2587 y Fj( )1320 2666 y Ft(1)p 1320 2710 V 1320 2802 a(2)1389 2666 y Fp(r)p Fm(\032)p Ft(\()p Fu(r)p Ft(\))p 1389 2710 255 4 v 1430 2802 a Fm(\032)p Ft(\()p Fu(r)p Ft(\))1676 2734 y(+)22 b Fp(j)p Fm(\025)p Fp(j)1904 2616 y Fj(Z)2002 2734 y Fm(d)2053 2692 y Fr(2)2093 2734 y Fu(r)2139 2692 y Fl(0)2162 2734 y Fm(\032)p Ft(\()p Fu(r)2296 2692 y Fl(0)2319 2734 y Ft(\))2414 2666 y Fu(r)g Fp(\000)h Fu(r)2628 2630 y Fl(0)p 2367 2710 332 4 v 2367 2802 a Fp(j)p Fu(r)e Fp(\000)i Fu(r)2608 2773 y Fl(0)2631 2802 y Fp(j)2659 2773 y Fr(2)2730 2734 y Fp(\000)g Fm(v)2938 2666 y Fu(r)f Fp(\000)h Fu(R)p 2891 2710 346 4 v 2891 2802 a Fp(j)p Fu(r)e Fp(\000)i Fu(R)p Fp(j)3198 2773 y Fr(2)3246 2587 y Fj(!)3312 2610 y Fr(2)3368 2734 y Fm(:)156 b Ft(\(3.17\))257 3013 y(Naime,)35 b(k)-5 b(ak)m(o)35 b(je)g(gusto)m(\023)-46 b(ca)35 b Fm(\032)p Ft(\()p Fu(r)p Ft(\))g(normirana)e(na)i Fm(N)45 b Ft(\(3.10\),)35 b(k)-5 b(anonski)35 b(k)m(onjugirani)f(momen)m(t)257 3193 y Fm(\031)t Ft(\()p Fu(r)p Ft(\))i(mora)e(i)m(\023)-46 b(ci)35 b(s)h(1)p Fm(=)-5 b(N)10 b Ft(,)36 b(e)g(da)g(bi)f(bila)f(zado) m(v)m(oljena)i(k)m(om)m(utacijsk)-5 b(a)36 b(relacija)e(\(3.9\).)52 b(Stoga,)36 b(u)257 3374 y(klasi)m(\024)-46 b(cnom)29 b(pribli)m(\024)-46 b(zenju)28 b(zanemarujeno)i(kineti)m(\024)-46 b(cki)26 b(\024)-46 b(clan.)41 b(Vidimo)28 b(da)h(je)h(u)m(\024)-46 b(cink)m(o)m(vni)31 b(p)s(otenci-)257 3554 y(jal)i(\(3.17\))g(p)s (ozitivno)g(de\014nitan,)i(te)f(je)g(na)5 b(jni)m(\024)-46 b(za)34 b(mogu)m(\023)-46 b(ca)33 b(vrijednost)h(k)m(o)5 b(ju)36 b(mo)m(\024)-46 b(ze)33 b(p)s(oprimiti)257 3735 y(jednak)-5 b(a)42 b(n)m(uli.)69 b(U)42 b(tom)e(slu)m(\024)-46 b(ca)5 b(ju)42 b(k)-5 b(a)m(\024)-46 b(zemo)41 b(da)g(smo)g(dosegli)f (Bogomol'n)m(yijevu)g(granicu,)j(te)257 3915 y(vrijedi)928 4029 y(1)p 928 4073 49 4 v 928 4164 a(2)997 4029 y Fp(r)p Fm(\032)1130 4044 y Fr(0)1169 4029 y Ft(\()p Fu(r)p Ft(\))p 997 4073 295 4 v 1038 4164 a Fm(\032)1088 4179 y Fr(0)1128 4164 y Ft(\()p Fu(r)p Ft(\))1323 4096 y(+)22 b Fp(j)p Fm(\025)p Fp(j)1551 3979 y Fj(Z)1650 4096 y Fm(d)1701 4055 y Fr(2)1740 4096 y Fu(r)1786 4055 y Fl(0)1809 4096 y Fm(\032)1859 4111 y Fr(0)1898 4096 y Ft(\()p Fu(r)1982 4055 y Fl(0)2005 4096 y Ft(\))2101 4029 y Fu(r)g Fp(\000)g Fu(r)2314 3992 y Fl(0)p 2053 4073 332 4 v 2053 4164 a Fp(j)p Fu(r)g Fp(\000)h Fu(r)2295 4136 y Fl(0)2318 4164 y Fp(j)2346 4136 y Fr(2)2417 4096 y Fp(\000)g Fm(v)2625 4029 y Fu(r)f Fp(\000)g Fu(R)p 2578 4073 346 4 v 2578 4164 a Fp(j)p Fu(r)f Fp(\000)h Fu(R)p Fp(j)2884 4136 y Fr(2)2961 4096 y Ft(=)27 b(0)p Fm(:)411 b Ft(\(3.18\))257 4330 y(Izra)m(\024)-46 b(cuna)5 b(jmo)33 b(div)m(ergenciju)g(gornjeg)f (izraza:)1307 4609 y(\001)17 b(ln)f Fm(\032)1553 4624 y Fr(0)1593 4609 y Ft(\()p Fu(r)p Ft(\))21 b(+)h(4)p Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(\032)2105 4624 y Fr(0)2144 4609 y Ft(\()p Fu(r)p Ft(\))27 b(=)h(4)p Fm(\031)t(v)t(\016)t Ft(\()p Fu(r)p Ft(\))p Fm(:)799 b Ft(\(3.19\))257 4888 y(U)36 b(slu)m(\024)-46 b(ca)5 b(ju)37 b(k)-5 b(ada)36 b(je)g Fm(v)h Ft(=)c(0,)k(gornja)e(jednad)m(\024)-46 b(zba)37 b(je)f(tzv.)55 b(Liouvilleo)m(v)-5 b(a)33 b(jednad)m(\024)-46 b(zba,)38 b(za)e(k)m(o)5 b(ju)257 5069 y(je)33 b(p)s(ok)-5 b(azano)32 b(da)h(su)g(sv)-5 b(a)33 b(rje)-5 b(\024)-44 b(senja)33 b(dana)f(izrazom:)1419 5348 y Fm(\032)1469 5363 y Fr(0)1509 5348 y Ft(\()p Fm(z)t(;)23 b Ft(\026)-55 b Fm(z)5 b Ft(\))28 b(=)1930 5280 y(2)p 1869 5324 172 4 v 1869 5416 a Fp(j)p Fm(\025)p Fp(j)p Fm(\031)2180 5280 y Fp(j)p Fm(f)2267 5244 y Fl(0)2290 5280 y Ft(\()p Fm(z)t Ft(\))p Fp(j)2443 5244 y Fr(2)p 2060 5324 542 4 v 2060 5416 a Ft([1)22 b(+)g Fp(j)p Fm(f)11 b Ft(\()p Fm(z)t Ft(\))p Fp(j)2496 5387 y Fr(2)2535 5416 y Ft(])2562 5387 y Fr(2)2612 5348 y Fm(;)912 b Ft(\(3.20\))p eop %%Page: 26 29 26 28 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(26)257 294 y(gdje)26 b(je)h Fm(f)11 b Ft(\()p Fm(z)t Ft(\))26 b(proizv)m(oljna)e(analiti)m(\024)-46 b(ck)-5 b(a)24 b(funk)m(cija,)j(izabrana)e(tak)m(o)h(da)g(je)g(gusto)m (\023)-46 b(ca)26 b Fm(\032)3312 309 y Fr(0)3378 294 y Ft(p)s(ozitivna,)257 474 y(nesingularna,)42 b(i)e(p)s(osebno)i(da)f (nema)f(p)s(olo)m(v)-5 b(a.)67 b(Kao)35 b(\024)-44 b(sto)42 b(smo)e(v)m(e)m(\023)-46 b(c)42 b(rekli,)g(nas)d(\023)-46 b(ce)41 b(zanimati)257 655 y(v)m(orteksna)i(rje)-5 b(\024)-44 b(senja,)45 b(dakle)c(gusto)m(\023)-46 b(ca)42 b Fm(\032)1783 670 y Fr(0)1861 655 y Ft(\023)-46 b(ce)42 b(u)g(nekim)f(to)m(\024)-46 b(ck)-5 b(ama)40 b(i)-5 b(\024)-44 b(s)m(\024)e(ceza)m(v)-5 b(ati.)70 b(Stoga)41 b(desna)257 835 y(strana)24 b(jednad)m(\024)-46 b(zb)s(e)24 b(\(3.19\))f(mora)f(u)h(tim)f(to)m(\024)-46 b(ck)-5 b(ama)22 b(kratiti)g(singularitete)f(k)m(o)5 b(ji)24 b(dolaze)e(o)s(d)f(\024)-46 b(clana)257 1016 y(\001)17 b(ln)f Fm(\032)503 1031 y Fr(0)543 1016 y Ft(\()p Fu(r)p Ft(\).)81 b(Radijalno)43 b(simetri)m(\024)-46 b(cno,)47 b(nenegativno)e(i)g(normalizabilno)c(rje)-5 b(\024)-44 b(senje)46 b(dobijemo)257 1197 y(uk)m(olik)m(o)39 b(uzmemo)f Fm(f)11 b Ft(\()p Fm(z)t Ft(\))38 b(=)g Fm(c)1369 1212 y Fi(n)1416 1197 y Fm(z)1465 1160 y Fl(\006)p Fi(n)1568 1197 y Ft(.)62 b(Uvrstimo)38 b(ta)5 b(j)39 b(izraz)f(za)h Fm(f)49 b Ft(u)39 b(\(3.20\),)h(pa)e(u)h(jednad)m(\024)-46 b(zbu)257 1377 y(\(3.19\))32 b(dobijemo)1058 1648 y Fm(\032)1108 1663 y Fr(0)1148 1648 y Ft(\()p Fm(r)s Ft(\))27 b(=)1412 1580 y(2\()p Fm(v)e Ft(+)d(1\))1756 1544 y Fr(2)p 1412 1624 384 4 v 1475 1716 a Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(r)1694 1687 y Fr(2)1822 1501 y Fj(")1870 1526 y(\022)1941 1580 y Fm(r)1985 1595 y Fr(0)p 1941 1624 84 4 v 1960 1716 a Fm(r)2035 1526 y Fj(\023)2096 1549 y Fr(\()p Fi(v)r Fr(+1\))2304 1648 y Ft(+)2402 1526 y Fj(\022)2491 1580 y Fm(r)p 2473 1624 V 2473 1716 a(r)2517 1731 y Fr(0)2566 1526 y Fj(\023)2628 1549 y Fr(\()p Fi(v)r Fr(+1\))2813 1501 y Fj(#)2862 1524 y Fl(\000)p Fr(2)2973 1648 y Fm(;)551 b Ft(\(3.21\))257 1927 y(gdje)42 b(smo)f(de\014nirali)f Fp(j)p Fm(c)1171 1942 y Fi(n)1218 1927 y Fp(j)j(\021)h Fm(r)1457 1877 y Fl(\000)p Fi(n=)p Fr(2)1454 1949 y(0)1629 1927 y Ft(.)71 b(Primjenimo)39 b(jo)-5 b(\024)-44 b(s)41 b(i)g(uvjet)i(normalizacije)38 b(gusto)m(\023)-46 b(ce)43 b Fm(\032)3761 1942 y Fr(0)257 2108 y Ft(\(3.10\),)30 b(\024)-46 b(cime)31 b(\014ksiramo)g("v)m(orticit)m(y")h Fm(v)g Ft(=)27 b Fm(N)10 b Fp(j)p Fm(\025)p Fp(j)p Fm(=)p Ft(2)22 b Fp(\000)g Ft(1)33 b(i)e(k)m(ona)m(\024)-46 b(cno)33 b(imamo)1157 2403 y Fm(\032)1207 2418 y Fr(0)1247 2403 y Ft(\()p Fm(r)s Ft(\))27 b(=)1510 2336 y Fp(j)p Fm(\025)p Fp(j)p Fm(N)1711 2300 y Fr(2)p 1510 2380 241 4 v 1533 2472 a Ft(2)p Fm(\031)t(r)1688 2443 y Fr(2)1777 2232 y Fj(2)1777 2382 y(4)1832 2282 y(\022)1903 2336 y Fm(r)1947 2351 y Fr(0)p 1903 2380 84 4 v 1922 2472 a Fm(r)1997 2282 y Fj(\023)2068 2271 y Ff(N)5 b Fe(j)p Ff(\025)p Fe(j)p 2068 2290 129 4 v 2117 2331 a Fc(2)2232 2403 y Ft(+)2330 2282 y Fj(\022)2420 2336 y Fm(r)p 2401 2380 84 4 v 2401 2472 a(r)2445 2487 y Fr(0)2495 2282 y Fj(\023)2566 2271 y Ff(N)g Fe(j)p Ff(\025)p Fe(j)p 2566 2290 129 4 v 2615 2331 a Fc(2)2708 2232 y Fj(3)2708 2382 y(5)2763 2255 y Fl(\000)p Fr(2)2874 2403 y Fm(:)650 b Ft(\(3.22\))257 2682 y(Ov)m(o)40 b(rje)-5 b(\024)-44 b(senje)41 b(opisuje)e Fm(n)h Ft(=)g(2\()p Fm(v)30 b Ft(+)d(1\))39 b(=)g Fm(N)10 b Fp(j)p Fm(\025)p Fp(j)40 b Ft(solitona)d(smje)-5 b(\024)-44 b(stenih)40 b(u)g(isho)s(di)-5 b(\024)-44 b(stu.)63 b(T)-8 b(reba)257 2863 y(uo)m(\024)-46 b(citi)31 b(da)i(op)m(\023)-46 b(cenito)32 b Fm(N)43 b Ft(nije)32 b(cijeli)e(bro)5 b(j,)33 b(ali)e Fm(v)36 b Ft(p)s(o)c(de\014niciji)f(jest.)404 3043 y(Lak)m(o)h(se)h(mo)m(\024) -46 b(zemo)30 b(uvjeriti)h(da)h(uk)m(olik)m(o)5 b(je)32 b Fm(N)43 b Ft(do)m(v)m(oljno)31 b(v)m(elik,)h(solitonsku)g(k)m (on\014guraciju)257 3224 y Fm(\032)307 3239 y Fr(0)380 3224 y Ft(mo)m(\024)-46 b(zemo)31 b(opisati)g Fm(\016)t Ft(-funk)m(cijom:)1583 3476 y Fm(\032)1633 3491 y Fr(0)1672 3476 y Ft(\()p Fm(r)s Ft(\))d(=)1946 3408 y Fm(N)p 1936 3452 108 4 v 1936 3544 a Ft(2)p Fm(\031)2064 3408 y(\016)t Ft(\()p Fm(r)c Fp(\000)f Fm(r)2361 3423 y Fr(0)2400 3408 y Ft(\))p 2064 3452 375 4 v 2209 3544 a Fm(r)2253 3559 y Fr(0)2448 3476 y Fm(:)1076 b Ft(\(3.23\))257 3727 y(Pri)32 b(izv)m(o)s(du)h(se)g(k)m(oristi)f(p)s(oznata)g(reprezen)m(tacija)h Fm(\016)t Ft(-funk)m(cije)1194 3979 y Fm(\016)t Ft(\()p Fm(x)p Ft(\))28 b(=)g(lim)1504 4036 y Fi(\017)p Fl(!)p Fr(0)1817 3912 y Ft(exp)q(\()p Fm(x=\017)p Ft(\))p 1666 3956 671 4 v 1666 4048 a Fm(\017)p 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Fl(0)2090 4844 y Fm(\032)2140 4859 y Fr(0)2180 4844 y Ft(\()p Fm(x)2273 4803 y Fl(0)2296 4844 y Ft(\)sign\()p Fm(x)g Fp(\000)h Fm(x)2773 4803 y Fl(0)2797 4844 y Ft(\))k(=)h(0)p Fm(;)509 b Ft(\(3.25\))257 5096 y(gdje)33 b(smo)f(isk)m(oristili)d(rezultat:)824 5230 y Fj(Z)907 5257 y Fi(L=)p Fr(2)870 5419 y Fl(\000)p Fi(L=)p Fr(2)1439 5280 y Fm(dy)1542 5244 y Fl(0)p 1074 5324 855 4 v 1074 5416 a Ft(\()p Fm(x)23 b Fp(\000)f Fm(x)1344 5387 y Fl(0)1368 5416 y Ft(\))1406 5387 y Fr(2)1468 5416 y Ft(+)g(\()p Fm(y)j Fp(\000)d Fm(y)1828 5387 y Fl(0)1851 5416 y Ft(\))1889 5387 y Fr(2)1966 5348 y Ft(=)2206 5280 y Fm(\031)p 2079 5324 312 4 v 2079 5416 a Fp(j)p Fm(x)h Fp(\000)f Fm(x)2339 5387 y Fl(0)2363 5416 y Fp(j)2423 5348 y Ft(+)g Fp(O)s Ft(\(1)p Fm(=L)p Ft(\))27 b Fm(;)45 b(x)28 b Fp(6)p Ft(=)f Fm(x)3183 5306 y Fl(0)3207 5348 y Fm(:)317 b Ft(\(3.26\))p eop %%Page: 27 30 27 29 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(27)257 294 y(Ograni)m(\024)-46 b(cili)32 b(smo)j(domen)m(u)h(k)m(olektivnog)g(p)s(olja)e Fm(\032)p Ft(\()p Fu(r)p Ft(\))h(na)h(proizv)m(oljno)e(v)m(elik,)j(ali) c(k)m(ona)m(\024)-46 b(can)37 b(in-)257 474 y(terv)-5 b(al)31 b(duljine)f Fm(L)p Ft(,)i(du)m(\024)-46 b(z)32 b Fm(y)i Ft(osi.)42 b(Uvijek)32 b(treba)f(imati)d(na)k(um)m(u)f(da)g (na)g(kra)5 b(ju)32 b(ra)m(\024)-46 b(cuna)31 b(pu)-5 b(\024)-44 b(stamo)257 655 y Fm(L)32 b Fp(!)f(1)k Ft(i)e Fm(N)42 b Fp(!)31 b(1)k Ft(isto)m(vremeno,)d(\024)-46 b(cuv)-5 b(a)5 b(ju)m(\023)-46 b(ci)35 b(omjer)f Fm(N)r(=L)h Ft(k)m(onstan)m(tnim,)g(ali)e(v)m(elikim)g(\(tzv.)257 835 y(termo)s(dinami)m(\024)-46 b(cki)29 b(limes\).)42 b(Derivira)5 b(jmo)30 b(izraz)i(\(3.25\))g(p)s(o)g(v)-5 b(arijabli)30 b Fm(x)p Ft(,)j(i)e(dobiv)-5 b(amo:)1367 1048 y(1)p 1367 1092 49 4 v 1367 1184 a(2)1463 1048 y Fm(@)1519 1012 y Fr(2)p 1436 1092 152 4 v 1436 1184 a Fm(@)5 b(x)1547 1155 y Fr(2)1614 1116 y Ft(ln)16 b Fm(\032)1762 1131 y Fr(0)1802 1116 y Ft(\()p Fm(x)p Ft(\))22 b(+)g(2)p Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(\032)2324 1131 y Fr(0)2363 1116 y Ft(\()p Fm(x)p Ft(\))28 b(=)f(0)p Fm(:)850 b Ft(\(3.27\))257 1396 y(Ov)-5 b(a)33 b(jednad)m(\024)-46 b(zba)33 b(p)s(osjeduje)g(p)s (ozitivno)e(i)h(normalizabilno)c(rje)-5 b(\024)-44 b(senje)1642 1676 y Fm(\032)1692 1691 y Fr(0)1731 1676 y Ft(\()p Fm(x)p Ft(\))28 b(=)2155 1609 y Fm(A)p 2004 1653 376 4 v 2004 1748 a Ft(cosh)2189 1706 y Fr(2)2245 1748 y Fm(B)5 b(x)2389 1676 y(;)1135 b Ft(\(3.28\))257 1956 y(gdje)33 b(je)1459 2137 y Fm(A)28 b Ft(=)1674 2069 y Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(N)1934 2033 y Fr(2)p 1674 2114 300 4 v 1746 2205 a Ft(2)p Fm(L)1861 2176 y Fr(2)2010 2137 y Fm(;)45 b(B)33 b Ft(=)2302 2069 y Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(N)p 2302 2114 260 4 v 2399 2205 a(L)2572 2137 y(:)952 b Ft(\(3.29\))257 2371 y(Rje)-5 b(\024)-44 b(senje)28 b(izgleda)c(p)s(oput)i(zida)g (visine)g Fm(A)p Ft(,)h(du)m(\024)-46 b(z)27 b Fm(y)j Ft(osi.)40 b(Kak)m(o)27 b Fm(N)36 b Ft(raste,)28 b(zidno)e(rje)-5 b(\024)-44 b(senje)27 b(p)s(osta)5 b(je)257 2552 y(sv)m(e)34 b(tanje,)f(o)s(dnosno,)g(za)g Fm(N)38 b Fp(!)27 b(1)32 b Ft(preuzima)g(oblik)f Fm(\016)t Ft(-)h(funk)m(cije)1696 2832 y Fm(\032)1746 2847 y Fr(0)1786 2832 y Ft(\()p Fm(x)p Ft(\))c(=)2058 2765 y Fm(N)p 2058 2809 89 4 v 2069 2900 a(L)2157 2832 y(\016)t Ft(\()p Fm(x)p Ft(\))p Fm(:)1189 b Ft(\(3.30\))257 3112 y(Gornji)34 b(izraz)g(lak)m(o)g(pro)m(vjerimo,)h (k)m(oriste)m(\023)-46 b(ci)34 b(izraz)h(\(3.24\),)g(gdje)g(je)g(sad)g (mali)d(parametar)i Fm(\017)e Ft(=)257 3293 y Fm(L=)p Ft(\(2)p Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(N)10 b Ft(\).)257 3717 y Fk(3.3)161 b(Kv)-9 b(an)l(tne)53 b(\015uktuacije)257 3996 y Ft(Razmotrimo)38 b(nadalje,)43 b(\015uktuacije)e(ok)m(o)h(rje)-5 b(\024)-44 b(senja)41 b(\(3.23\),)i(o)s(dnosno)e(razvijmo)f(k)m (olektivno)257 4177 y(p)s(olje)32 b Fm(\032)p Ft(\()p Fu(r)p Ft(\))1611 4357 y Fm(\032)p Ft(\()p Fu(r)p Ft(\))c(=)g Fm(\032)1965 4372 y Fr(0)2004 4357 y Ft(\()p Fu(r)p Ft(\))22 b(+)g Fm(\021)t Ft(\()p Fu(r)p Ft(\))p Fm(;)1104 b Ft(\(3.31\))257 4592 y(gdje)38 b(je)g Fm(\021)t Ft(\()p Fu(r)p Ft(\))f(mala)f(\(u)i(1)p Fm(=)-5 b(N)47 b Ft(razv)m(o)5 b(ju\))39 b(kv)-5 b(an)m(tna)38 b(p)s(opra)m(vk)-5 b(a,)39 b(o)s(dnosno)f(\015uktuacija)g(gusto)m(\023) -46 b(ce)257 4773 y(ok)m(o)38 b Fm(\032)491 4788 y Fr(0)531 4773 y Ft(\()p Fu(r)p Ft(\).)57 b(Uvrstimo)36 b(razv)m(o)5 b(j)38 b(\(3.31\))e(u)i(\(3.16\),)f(te)h(razvijmo)e(do)h(kv)-5 b(adrati)m(\024)-46 b(cnih)33 b(\024)-46 b(clano)m(v)-5 b(a)36 b(u)257 4953 y Fm(\021)t Ft(\()p Fu(r)p Ft(\),)44 b(i)c(dobit)e(\023)-46 b(cemo)41 b(v)m(o)s(de)m(\023)-46 b(ci)40 b(\024)-46 b(clan)40 b Fm(V)1674 4968 y Fr(u)n(\024)-33 b(c)q(in)1808 4953 y Ft(\()p Fm(\032)1896 4968 y Fr(0)1935 4953 y Ft(\))42 b(i)f(hamiltonijan)c(kv)-5 b(adrati)m(\024)-46 b(can)42 b(u)f(p)s(olju)g Fm(\021)t Ft(\()p Fu(r)p Ft(\))g(i)257 5134 y(njem)m(u)34 b(k)-5 b(anonski)34 b(k)m(onjugiranom)e(p)s(olju)g Fm(\031)t Ft(\()p Fu(r)p Ft(\).)2085 5108 y(\024)2074 5134 y(Clano)m(v)-5 b(a)33 b(linearnih)e(u)j(p)s(olju)e Fm(\021)t Ft(\()p Fu(r)p Ft(\))h(nema,)h(jer)p eop %%Page: 28 31 28 30 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(28)257 294 y(razvijamo)31 b(ok)m(o)i(ekstrema.)306 585 y Fm(H)i Ft(=)48 b Fm(V)603 600 y Fr(u)n(\024)-33 b(cin)736 585 y Ft(\()p Fm(\032)824 600 y Fr(0)864 585 y Ft(\))22 b(+)1032 518 y(1)p 1032 562 49 4 v 1032 654 a(2)1108 468 y Fj(Z)1207 585 y Fm(d)1258 544 y Fr(2)1297 585 y Fu(r)p Fm(\032)1393 600 y Fr(0)1433 585 y Ft(\()p Fu(r)p Ft(\))1572 439 y Fj(")1622 559 y Ft(^)1619 585 y Fm(k)k Fp(\002)c(r)p Fm(\031)k Fp(\000)2069 518 y Ft(1)p 2069 562 V 2069 654 a(2)2128 585 y Fp(r)2228 439 y Fj( )2322 518 y Fm(\021)t Ft(\()p Fu(r)p Ft(\))p 2303 562 212 4 v 2303 654 a Fm(\032)2353 669 y Fr(0)2393 654 y Ft(\()p Fu(r)p Ft(\))2524 439 y Fj(!)2612 585 y Fp(\000)d(j)p Fm(\025)p Fp(j)2842 468 y Fj(Z)2940 585 y Fm(d)2991 544 y Fr(2)3030 585 y Fu(r)3076 544 y Fl(0)3100 585 y Fm(\021)t Ft(\()p Fu(r)3236 544 y Fl(0)3258 585 y Ft(\))3354 518 y Fu(r)e Fp(\000)i Fu(r)3567 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1490 y Fr(0)1846 1407 y Ft(+)22 b Fp(j)p Fm(\025)p Fp(j)2074 1290 y Fj(Z)2173 1407 y Fm(d)2224 1366 y Fr(2)2263 1407 y Fu(r)2309 1366 y Fl(0)2349 1407 y Ft(ln)16 b Fp(j)p Fm(z)26 b Fp(\000)d Fm(z)2695 1366 y Fl(0)2719 1407 y Fp(j)p Fm(\021)t Ft(\()p Fm(z)2886 1366 y Fl(0)2909 1407 y Ft(\))2947 1261 y Fj(!)3029 1407 y Fm(;)819 1689 y(A)892 1648 y Fl(y)927 1689 y Ft(\()p Fm(z)t Ft(\))29 b(=)1194 1622 y Fm(@)5 b(\031)p 1194 1666 116 4 v 1199 1758 a(@)11 b Ft(\026)-55 b Fm(z)1342 1689 y Ft(+)22 b Fm(i)1508 1622 y(@)p 1483 1666 107 4 v 1483 1758 a(@)11 b Ft(\026)-55 b Fm(z)1617 1543 y Fj( )1736 1622 y Fm(\021)p 1692 1666 139 4 v 1692 1758 a Ft(2)p Fm(\032)1791 1773 y Fr(0)1863 1689 y Ft(+)22 b Fp(j)p Fm(\025)p Fp(j)2091 1572 y Fj(Z)2190 1689 y Fm(d)2241 1648 y Fr(2)2280 1689 y Fu(r)2326 1648 y Fl(0)2365 1689 y Ft(ln)16 b Fp(j)p Fm(z)27 b Fp(\000)22 b Fm(z)2711 1648 y Fl(0)2735 1689 y Fp(j)p Fm(\021)t Ft(\()p Fm(z)2902 1648 y Fl(0)2926 1689 y Ft(\))2964 1543 y Fj(!)3046 1689 y Fm(;)478 b 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5211 a Fo(1)407 5242 y Fn(Dalje)57 b(u)f(tekstu)h(p)r(o)r(drazumijev)-5 b(amo)55 b(da)i(o)n(visnost)d(funk)n(cija)j(i)f(op)r(eratora)f(o)h Fh(z)t Fn(,)62 b(zapra)n(v)n(o)54 b(zna)n(\024)-39 b(ci)257 5391 y(funk)n(cionaln)n(u)27 b(o)n(visnost)f(o)i Fh(z)j Fn(i)h(\026)-47 b Fh(z)t Fn(.)p eop %%Page: 29 32 29 31 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(29)257 294 y(Zah)m(tjev)-5 b(amo)50 b(da)g(hamiltonijan)d(\(3.36\))j(bude)h(dijagonalan)d(u)j(tim) d(no)m(vim)i(op)s(eratorima,)257 474 y(o)s(dnosno)33 b(da)f(vrijedi:)1682 655 y Fm(H)j Ft(=)1901 572 y Fj(X)1939 746 y Fd(n)2038 655 y Fm(!)2099 670 y Fd(n)2148 655 y Fm(a)2199 614 y Fl(y)2199 680 y Fd(n)2249 655 y Fm(a)2300 670 y Fd(n)2349 655 y Fm(:)1175 b Ft(\(3.39\))257 878 y(U)45 b(gornjim)d(izrazima,)j Fu(n)j Ft(=)g(\()p Fm(n)1509 893 y Fr(1)1548 878 y Fm(;)17 b(n)1650 893 y Fr(2)1690 878 y Ft(\))44 b(predsta)m(vlja)h(par)f(kv)-5 b(an)m(tnih)44 b(bro)5 b(jev)-5 b(a,)48 b(te)d(u)f(slu)m(\024)-46 b(ca)5 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Fm(x;)g(y)t Ft(\))p Fm(:)1757 b Ft(\(3.51\))p eop %%Page: 32 35 32 34 bop 257 -89 a Fs(3.)44 b(CHERN-SIMONSO)m(V)-11 b(A)34 b(TEORIJA)1874 b Ft(32)257 294 y(Kak)m(o)42 b(op)s(erator)f(na)h (desno)5 b(j)43 b(strani)e(gornje)g(jednad)m(\024)-46 b(zb)s(e)43 b(k)m(om)m(utira)e(s)h Fm(p)2997 309 y Fi(y)3082 294 y Ft(=)h Fp(\000)p Fm(i@)3362 309 y Fi(y)3404 294 y Ft(,)i(tra)m(\024)-46 b(zimo)257 474 y(rje)-5 b(\024)-44 b(senje)34 b(u)f(obliku)e(\011)1068 489 y Fd(n)1117 474 y Ft(\()p Fm(x;)17 b(y)t Ft(\))27 b(=)h(exp)q(\()p Fp(\006)p Fm(iny)t Ft(\))p Fm( )1983 489 y Fr(0)p Fi(;n)2085 474 y Ft(\()p Fm(x)p Ft(\),)33 b(te)g(dobiv)-5 b(amo)257 755 y Fm(!)318 770 y Fi(n)365 755 y Fm( )428 770 y Fr(0)p Fi(;n)530 755 y Ft(\()p Fm(x)p Ft(\))28 b(=)g Fp(\000)880 687 y Ft(1)p 880 731 49 4 v 880 823 a(2)939 755 y Fm(@)995 713 y Fr(2)990 779 y Fi(x)1035 755 y Fm( )1098 770 y Fr(0)p Fi(;n)1201 755 y Ft(\()p Fm(x)p Ft(\))p Fp(\006)p Fm(n)g Ft(sign\()p Fm(x)p Ft(\)\003)1863 770 y Fi(N)1930 755 y Fm( )1993 770 y Fr(0)p Fi(;n)2095 755 y Ft(\()p Fm(x)p Ft(\)+)2312 687 y(1)p 2312 731 V 2312 823 a(2)2371 755 y(\()p Fm(n)2467 713 y Fr(2)2507 755 y Ft(+\003)2651 713 y Fr(2)2651 779 y Fi(N)2718 755 y Ft(\))p Fm( )2819 770 y Fr(0)p Fi(;n)2921 755 y Ft(\()p Fm(x)p Ft(\))p Fp(\000j)p Fm(\025)p Fp(j)p Fm(\031)t(\032)3351 770 y Fr(0)3391 755 y Ft(\()p Fm(x)p Ft(\))p Fm( )3585 770 y Fr(0)p Fi(;n)3687 755 y Ft(\()p Fm(x)p Ft(\))p Fm(;)3551 935 y Ft(\(3.52\))257 1116 y(gdje)33 b(smo)f(uv)m(eli)g(p)s(okratu)1753 1229 y Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(N)p 1753 1273 260 4 v 1849 1365 a(L)2050 1296 y Ft(=)27 b(\003)2221 1311 y Fi(N)2288 1296 y Fm(:)257 1531 y Ft(Predznak)35 b(u)d(fazi)g(funk)m(cije)h(\011)1397 1546 y Fd(n)1446 1531 y Ft(\()p Fm(x;)17 b(y)t Ft(\))32 b(biramo)e(tak)m(o)j(da)g (dobijemo)503 1811 y Fm(!)564 1826 y Fi(n)611 1811 y Fm( )674 1826 y Fr(0)p Fi(;n)776 1811 y Ft(\()p Fm(x)p Ft(\))28 b(=)g Fp(\000)1126 1744 y Ft(1)p 1126 1788 49 4 v 1126 1879 a(2)1185 1811 y Fm(@)1241 1770 y 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b(ju.)75 b(Jednad)m(\024)-46 b(zbu)45 b(\(3.53\))e(rje)-5 b(\024)-44 b(sa)m(v)-5 b(a)257 2633 y(funk)m(cija)35 b Fm( )691 2648 y Fr(0)p Fi(;n)793 2633 y Ft(\()p Fm(x)p Ft(\))c(=)1061 2556 y Fp(p)p 1144 2556 135 4 v 77 x Ft(\003)1212 2648 y Fi(N)1296 2633 y Ft(exp)q(\()p Fp(\000)p Ft(\003)1628 2648 y Fi(N)1695 2633 y Fp(j)p Fm(x)p Fp(j)p Ft(\),)k(i)e(tak)m(o)i(za) f(vlastite)g(frekv)m(encije)h(malih)d(oscilacija)257 2813 y(ok)m(o)h(rje)-5 b(\024)-44 b(senja)33 b(\(3.30\))f(dobiv)-5 b(amo:)1556 3094 y Fm(!)1617 3109 y Fi(n)1692 3094 y Ft(=)1805 3026 y(1)p 1805 3070 49 4 v 1805 3162 a(2)1864 3094 y Fm(n)1922 3053 y Fr(2)1984 3094 y Ft(+)2092 3026 y Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t(N)p 2092 3070 260 4 v 2188 3162 a(L)2361 3094 y Fp(j)p Fm(n)p Fp(j)p Fm(:)1049 b Ft(\(3.54\))p eop %%Page: 33 36 33 35 bop 257 1082 a Fv(P)-6 b(ogla)g(vlje)76 b(4)257 1622 y(Diskusija)257 2135 y Ft(U)46 b(pretho)s(dna)g(dv)-5 b(a)45 b(p)s(ogla)m(vlja)f(izlo)m(\024)-46 b(zili)41 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y(mehanizam.)i(T)-8 b(o)28 b(p)s(o)s(drazumjev)-5 b(a)27 b(k)m(ompakti\014k)-5 b(aciju)26 b(jedne)j(\(na)5 b(j)m(\024)-46 b(ce)-5 b(\024)-44 b(s)m(\023)e(ce)30 b(prostorne\))f(dimenzi-)257 5005 y(je,)g(nametanje)f(o)s(dred)p 1062 4953 V(enih)g(rubnih)g(uvjeta)g(na)g(p)s(olja)e(u)i(problem)m(u,)h (iden)m(ti\014k)-5 b(aciju)26 b(k)m(omp)s(one-)257 5186 y(nata)g(p)s(olja)f(k)-5 b(ao)26 b(no)m(vih,)h(neza)m(visnih)g (stupnjev)-5 b(a)27 b(slob)s(o)s(de)f(u)g(ni)m(\024)-46 b(zedimenzijsk)m(om)25 b(problem)m(u,)i(te)257 5366 y(rein)m (terpretaciju)e(sp)s(ektra)g(p)s(obud)p 1510 5314 V(enja.)42 b(T)-8 b(a)24 b(ideja)g(o)s(d)h(sv)m(o)5 b(je)26 b(p)s(o)5 b(ja)m(v)m(e)26 b(dv)-5 b(adesetih)25 b(go)s(dina)e(o)m(v)m(og)1980 5674 y(33)p eop %%Page: 34 37 34 36 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(34)257 294 y(stolje)m(\023)-46 b(ca)38 b(privla)m(\024)-46 b(ci)36 b(izuzetno)j(puno)f(pa)m(\024)-46 b(znje,)40 b(jer)e(se)h(uvidjelo)e (da)i(u)f(v)m(e)m(\023)-46 b(cem)39 b(bro)5 b(ju)39 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b(tj.)57 b(iden)m(ti\014cira) 35 b(se)j(k)m(ompleksna,)h(Bargmann-F)-8 b(o)s(c)m(k)m(o)m(v)j(a)35 b(reprezen)m(tacija)j(algebre)e(o-)257 4808 y(p)s(eratora)c(u)h(danim)e (mo)s(delima)e([27].)404 4989 y(T)-8 b(ak)m(o)s(d)p 634 4936 V(er)44 b(je)f(p)s(ok)-5 b(azano)43 b(se)i(da)e(osno)m(vno)h (stanje)g(u)g(Calogero-Sutherlando)m(v)m(om)e(mode-)257 5169 y(lu)e(i)f(Lauglino)m(v)m(o)g(stanje)h(u)g(F)m(QH)g(u)m(\024)-46 b(cinku)41 b(p)s(o)s(dudara)5 b(ju)40 b(na)g(geometriji)d(usk)m(og)k(v) -5 b(aljk)g(a)39 b([28)o(].)257 5350 y(Koriste)m(\023)-46 b(ci)36 b(hidro)s(dinami)m(\024)-46 b(cku)35 b(k)m(olektivn)m(u)j (teoriju)e(p)s(olja,)h(author)f(rada)h([29])g(su)h(p)s(ok)-5 b(azali)35 b(da)p eop %%Page: 35 38 35 37 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(35)257 294 y(k)m(orelacijsk)m(e)40 b(funk)m(cije)h(fermiona)c(na)j(rubu)g(F)m (QH)f(uzork)-5 b(a)40 b(prelaze)f(u)h(k)m(orelacijsk)m(e)g(funk)m(cije) 257 474 y(u)k(Calogero)m(v)m(om)f(mo)s(delu)f(k)-5 b(ak)m(o)44 b(se)c(\024)-44 b(sirina)42 b(uzork)-5 b(a)44 b(smanjuje.)77 b(Kona)m(\024)-46 b(cno,)46 b(F)m(QH)e(u)m(\024)-46 b(cinak)44 b(i)257 655 y(Calogero-Sutherlando)m(v)h(mo)s(del)g(dijele)f(istu,)49 b(b)s(esk)m(ona)m(\024)-46 b(cno)48 b(dimenzionaln)m(u)c Fm(W)3366 670 y Fl(1)3486 655 y Ft(algebru)257 835 y([30].)404 1016 y(Instruktivno)32 b(je)g(p)s(ogledati)d(k)-5 b(ak)m(o)32 b(jak)m(o)f(magnetsk)m(o)h(p)s(olje)f(v)m(o)s(di)g(na)g(dimenzijsku)g (reduk-)257 1197 y(ciju)h(u)h(sistem)m(u.)44 b(Razmotrimo)29 b(hamiltonijan)d(\024)-46 b(cestice)33 b(u)g(magnetsk)m(om)f(p)s(olju) 1188 1471 y Fm(H)1269 1486 y Fr(0)1336 1471 y Ft(=)1464 1388 y Fj(X)1439 1571 y Fi(i)p Fr(=1)p Fi(;)p Fr(2)1635 1404 y Ft(\(\005)1746 1419 y Fi(i)1774 1404 y Ft(\))1812 1368 y Fr(2)p 1635 1448 217 4 v 1676 1540 a Ft(2)p Fm(m)1862 1471 y(;)44 b Ft(\005)2006 1486 y Fi(i)2062 1471 y Ft(=)28 b Fm(p)2215 1486 y Fi(i)2265 1471 y Fp(\000)23 b Fm(A)2438 1486 y Fi(i)2466 1471 y Fm(;)44 b(i)28 b Ft(=)g(1)p Fm(;)17 b Ft(2)p Fm(:)257 1764 y 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b(uk)m(olik)m(o)d(je)h(razmak)f (energijskih)h(niv)m(ou)g(zb)s(og)f(v)-5 b(anjsk)m(og)47 b(p)s(otencijala)257 5030 y(\(recimo)g Fm(V)22 b Ft(\()p Fm(y)t Ft(\)\))47 b(v)m(elik,)k(u)d(usp)s(oredbi)h(s)f(energijom)e Fm(E)2379 5045 y Fi(x)2478 5030 y Ft(=)53 b Fm(p)2656 4994 y Fr(2)2656 5054 y Fi(x)2700 5030 y Fm(=)p Ft(2)p Fm(m)p Ft(,)f(i)44 b(\024)-46 b(cestice)49 b(su)g(dalek)m(o,)257 5210 y(mo)m(\024)-46 b(zemo)30 b(zanemariti)g(sv)-5 b(a,)32 b(osim)d(na)5 b(jni)m(\024)-46 b(zeg,)32 b(vlastita)e(stanja)h(u)h Fm(y)i Ft(smjeru,)e(i)e(tak)m(o)i(u)m(\024)-46 b(cink)m(o)m(vno)257 5391 y(dobiv)-5 b(amo)31 b(jedno)s(dimenzijski)g(sistem.)p eop %%Page: 36 39 36 38 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(36)404 294 y(Na)-5 b(\024)-44 b(s)22 b(rezultat)g(je)g(na)g(tom)f(tragu.)39 b(Naime,)23 b(ak)m(o)g(se)f(prisjetmo)f(rezultata)h(pro)-5 b(\024)-44 b(slog)21 b(p)s(ogla)m(vlja,)257 474 y(gdje)29 b(smo)e(izv)m(eli)g(izraz)g(za)i(\015uktuacije)f(ok)m(o)g(osno)m(vnog)h 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b(u)f(radu)h([32)o(],)g(gdje)g(smo)f(usp)s (osta)m(vili)257 2822 y(v)m(ezu)41 b(izmed)p 701 2769 V(u)e(hamiltonijana)d(Calogero)m(v)m(og)j(mo)s(dela)f(i)g(Jac)m(kiw-Pi) h(mo)s(dela,)h(u)f(form)m(ulaciji)257 3002 y(k)m(olektivne)34 b(teorije)e(p)s(olja.)43 b(Kren)m(uli)32 b(smo)h(o)s(d)g("zidnog")e (rje)-5 b(\024)-44 b(senja)34 b(\(3.30\))e(u)i(Jac)m(kiw-Pi)e(mo)s(d-) 257 3183 y(elu,)g(te)g(smo)f(pretp)s(osta)m(vili)f(da)i(kv)-5 b(an)m(tne)32 b(\015uktuacije)g(sadr)m(\024)-46 b(ze)33 b(rje)-5 b(\024)-44 b(senje)33 b(osno)m(vnog)f(stanja)g(k)-5 b(ao)257 3363 y(faktor,)33 b(te)g(da)f(mo)m(\024)-46 b(zemo)31 b(razdv)m(o)5 b(jiti)32 b Fm(x)h Ft(i)f Fm(y)j Ft(o)m(visnost)e(gusto)m(\023)-46 b(ce)34 b(\015uktuacija:)918 3644 y Fm(\032)p Ft(\()p Fu(r)p Ft(\))28 b(=)f Fm(\032)1271 3659 y Fr(0)1311 3644 y Ft(\()p Fu(r)p Ft(\))22 b(+)g Fm(\021)t Ft(\()p Fu(r)p Ft(\))27 b(=)g Fm(\032)1907 3659 y Fr(0)1947 3644 y Ft(\()p Fu(r)p Ft(\))22 b(+)g Fm(\032)2239 3659 y Fr(0)2279 3644 y Ft(\()p Fm(x)p 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201 4 v 1470 4752 a Fm(L)1631 4566 y Fj(Z)1730 4683 y Fm(dx)1836 4642 y Fl(0)1860 4683 y Fm(dy)1963 4642 y Fl(0)1985 4683 y Fm(\016)t Ft(\()p Fm(x)2125 4642 y Fl(0)2148 4683 y Ft(\))f(~)-58 b Fm(\032)q Ft(\()p Fm(y)2327 4642 y Fl(0)2349 4683 y Ft(\))2700 4616 y Fm(y)25 b Fp(\000)e Fm(y)2925 4580 y Fl(0)p 2397 4660 855 4 v 2397 4752 a Ft(\()p Fm(x)f Fp(\000)h Fm(x)2667 4723 y Fl(0)2691 4752 y Ft(\))2729 4723 y Fr(2)2790 4752 y Ft(+)f(\()p Fm(y)j Fp(\000)e Fm(y)3151 4723 y Fl(0)3173 4752 y Ft(\))3211 4723 y Fr(2)3261 4537 y Fj(#)3309 4560 y Fr(2)479 4966 y Ft(+)578 4898 y Fm(N)p 565 4942 116 4 v 565 5034 a Ft(2)p Fm(L)707 4849 y Fj(Z)806 4966 y Fm(dxdy)t(\016)t Ft(\()p Fm(x)p Ft(\))9 b(~)-58 b Fm(\032)p Ft(\()p Fm(y)t Ft(\))1388 4820 y Fj(")1445 4898 y Fm(@)5 b(\031)p 1445 4942 V 1449 5034 a(@)g(y)1593 4966 y Ft(+)1701 4898 y(1)p 1701 4942 49 4 v 1701 5034 a(2)1797 4898 y Fm(@)p 1769 4942 113 4 v 1769 5034 a(@)g(x)1908 4966 y Ft(ln)16 b Fm(\032)2056 4981 y Fr(0)2096 4966 y Ft(\()p Fm(x)p Ft(\))1316 5265 y(+)1402 5197 y Fm(N)10 b Fp(j)p Fm(\025)p Fp(j)p 1402 5241 201 4 v 1469 5333 a Fm(L)1629 5147 y Fj(Z)1729 5265 y Fm(dx)1835 5223 y Fl(0)1858 5265 y Fm(dy)1961 5223 y Fl(0)1983 5265 y Fm(\016)t Ft(\()p Fm(x)2123 5223 y Fl(0)2147 5265 y Ft(\))f(~)-58 b Fm(\032)p Ft(\()p Fm(y)2325 5223 y Fl(0)2347 5265 y Ft(\))2694 5197 y Fm(x)23 b Fp(\000)f Fm(x)2926 5161 y Fl(0)p 2395 5241 855 4 v 2395 5333 a Ft(\()p Fm(x)h Fp(\000)f Fm(x)2665 5304 y Fl(0)2689 5333 y Ft(\))2727 5304 y Fr(2)2789 5333 y Ft(+)g(\()p Fm(y)j Fp(\000)d Fm(y)3149 5304 y Fl(0)3172 5333 y Ft(\))3210 5304 y Fr(2)3259 5118 y Fj(#)3308 5141 y Fr(2)3364 5265 y Fm(:)209 b Ft(\(4.2\))p eop %%Page: 37 40 37 39 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(37)257 294 y(Uzima)5 b(ju)m(\023)-46 b(ci)40 b(u)h(obzir)f(jednad)m(\024)-46 b(zbu)42 b(\(3.25\))e(i)g(oblik)g(rje)-5 b(\024)-44 b(senja)42 b(za)f Fm(\032)2714 309 y Fr(0)2753 294 y Ft(\()p Fm(x)p Ft(\),)j(dan)d(izrazom)e(\(3.30\),)257 474 y(in)m(terpretiramo)31 b(izraz)h Fm(@)1189 489 y Fi(x)1250 474 y Ft(ln)16 b Fm(\032)1398 489 y Fr(0)1438 474 y Ft(\()p Fm(x)p Ft(\))32 b(k)-5 b(ao)33 b Fp(\000)p Ft(2)p Fm(N)10 b Fp(j)p Fm(\025)p Fp(j)p Fm(\031)t Ft(sign)o(\()p Fm(x)p Ft(\))p Fm(=L)p Ft(,)28 b(\024)-44 b(sto)33 b(nam)f(da)5 b(je)654 746 y Fm(H)55 b Ft(=)917 679 y Fm(N)p 903 723 116 4 v 903 815 a Ft(2)p Fm(L)1045 629 y Fj(Z)1145 746 y Fm(dy)12 b Ft(~)-57 b Fm(\032)o Ft(\()p Fm(y)t Ft(\))1442 600 y Fj(")1509 679 y Fm(@)5 b(\031)p 1509 723 V 1511 815 a(@)g(x)1635 597 y Fj(\014)1635 647 y(\014)1635 696 y(\014)1635 746 y(\014)1635 796 y(\014)1662 850 y Fi(x)p Fr(=0)1819 746 y Fp(\000)1928 679 y Ft(1)p 1928 723 49 4 v 1928 815 a(2)2022 679 y Fm(@)p 1997 723 109 4 v 1997 815 a(@)g(y)2131 746 y Ft(ln)25 b(~)-58 b Fm(\032)q Ft(\()p Fm(y)t Ft(\))21 b Fp(\000)2538 679 y Fm(N)10 b Fp(j)p Fm(\025)p Fp(j)p 2538 723 201 4 v 2606 815 a Fm(L)2749 746 y Fp(\000)2748 629 y Fj(Z)2832 746 y Fm(dy)2935 705 y Fl(0)3037 679 y Ft(~)-58 b Fm(\032)p Ft(\()p Fm(y)3168 643 y Fl(0)3191 679 y Ft(\))p 2967 723 324 4 v 2967 815 a(\()p Fm(y)25 b Fp(\000)e Fm(y)3230 786 y Fl(0)3252 815 y Ft(\))3300 600 y Fj(#)3348 623 y Fr(2)908 1058 y Ft(+)1007 990 y Fm(N)p 994 1034 116 4 v 994 1126 a Ft(2)p Fm(L)1136 940 y Fj(Z)1235 1058 y Fm(dy)12 b Ft(~)-57 b Fm(\032)o Ft(\()p Fm(y)t Ft(\))1541 911 y Fj( )1617 990 y Fm(@)5 b(\031)p 1617 1034 V 1621 1126 a(@)g(y)1742 911 y Fj(!)1808 934 y Fr(2)1848 883 y Fj(\014)1848 933 y(\014)1848 983 y(\014)1848 1033 y(\014)1848 1082 y(\014)1848 1132 y(\014)1875 1186 y Fi(x)p Fr(=0)2026 1058 y Fm(:)1547 b Ft(\(4.3\))257 1340 y(In)m(tegral)44 b(p)s(o)g Fm(y)834 1304 y Fl(0)900 1340 y Ft(u)h(gornjem)e(izrazu)h(izvrijednit)c(\023)-46 b(cemo)43 b(k)-5 b(ao)44 b(gla)m(vn)m(u)g(vrijednost)g(in)m(tegrala.) 257 1521 y(Naime,)27 b(zb)s(og)f(prisustv)-5 b(a)26 b Fm(\016)t Ft(-)g(funk)m(cije)g(jezgra)h(in)m(tegrala)d(u)j(prv)m(om)c (\024)-46 b(clan)m(u)26 b(hamiltonijana)c(\(4.2\))1439 1707 y Fm(y)k Fp(\000)c Fm(y)1664 1671 y Fl(0)p 1136 1751 855 4 v 1136 1843 a Ft(\()p Fm(x)g Fp(\000)h Fm(x)1406 1814 y Fl(0)1430 1843 y Ft(\))1468 1814 y Fr(2)1529 1843 y Ft(+)f(\()p Fm(y)k Fp(\000)c Fm(y)1890 1814 y Fl(0)1913 1843 y Ft(\))1951 1814 y Fr(2)2055 1774 y Ft(ide)55 b(u)2487 1707 y Fm(y)26 b Fp(\000)c Fm(y)2712 1671 y Fl(0)p 2327 1751 568 4 v 2327 1843 a Fm(")2373 1814 y Fr(2)2434 1843 y Ft(+)g(\()p Fm(y)k Fp(\000)c Fm(y)2795 1814 y Fl(0)2818 1843 y Ft(\))2856 1814 y Fr(2)2905 1774 y Fm(;)257 2028 y Ft(k)-5 b(ak)m(o)33 b Fm(")f Ft(ide)h(u)f(n)m(ulu,)h(pa)f(p)s(o)h (de\014niciji)d(imamo)1407 2281 y(lim)1405 2338 y Fi(")p Fl(!)p Fr(0)1731 2214 y Fm(y)25 b Fp(\000)d Fm(y)1955 2177 y Fl(0)p 1570 2258 V 1570 2349 a Fm(")1616 2321 y Fr(2)1677 2349 y Ft(+)h(\()p Fm(y)i Fp(\000)d Fm(y)2038 2321 y Fl(0)2061 2349 y Ft(\))2099 2321 y Fr(2)2176 2281 y Fp(\021)28 b(P)2468 2214 y Ft(1)p 2368 2258 248 4 v 2368 2349 a Fm(y)e Fp(\000)c Fm(y)2593 2321 y Fl(0)2626 2281 y Fm(:)257 2534 y Ft(Ima)5 b(ju)m(\023)-46 b(ci)37 b(na)g(um)m(u)g(k)m(om)m(utator)f(\(3.9\))h(i)f(strukturu)i(\(4.1\))f (gusto)m(\023)-46 b(ce)38 b Fm(\032)p Ft(\()p Fu(r)p Ft(\),)g(mo)m(\024)-46 b(zemo)36 b(p)s(ok)-5 b(azati,)257 2715 y(k)m(oriste)m(\023)-46 b(ci)23 b(lan)m(\024)-46 b(cano)22 b(pra)m(vilo)g(funk)m(cionalnog)f(deriviranja,)j(da)f(se)g(k) -5 b(anonski)23 b(impuls)e Fm(\031)t Ft(\()p Fu(r)p Ft(\))i(trans-)257 2895 y(formira)31 b(u)468 3149 y Fm(\031)t Ft(\()p Fu(r)p Ft(\))c Fp(\021)i(\000)p Fm(i)988 3081 y(\016)p 902 3126 219 4 v 902 3217 a(\016)t(\032)p Ft(\()p Fu(r)p Ft(\))1159 3149 y(=)e Fp(\000)p Fm(i)1389 3032 y Fj(Z)1489 3149 y Fm(dz)1599 3081 y(\016)13 b Ft(~)-58 b Fm(\032)q Ft(\()p Fm(z)t Ft(\))p 1599 3126 223 4 v 1601 3217 a Fm(\016)t(\032)p Ft(\()p Fu(r)p Ft(\))1931 3081 y Fm(\016)p 1843 3126 V 1843 3217 a(\016)13 b Ft(~)-58 b Fm(\032)p Ft(\()p Fm(z)t Ft(\))2103 3149 y(=)28 b Fp(\000)p Fm(i)2352 3081 y(\016)t Ft(\(0\))p 2327 3126 222 4 v 2327 3217 a Fm(\032)2377 3232 y Fr(0)2417 3217 y Ft(\()p Fm(x)p Ft(\))2657 3081 y Fm(\016)p 2568 3126 225 4 v 2568 3217 a(\016)13 b Ft(~)-58 b Fm(\032)q Ft(\()p Fm(y)t Ft(\))2830 3149 y Fp(\021)2970 3081 y Fm(\016)t Ft(\(0\))p 2945 3126 222 4 v 2945 3217 a Fm(\032)2995 3232 y Fr(0)3035 3217 y Ft(\()p Fm(x)p Ft(\))3181 3149 y(~)k Fm(\031)t Ft(\()p Fm(y)t Ft(\))p Fm(:)210 b Ft(\(4.4\))257 3402 y(Sli)m(\024)-46 b(cno)32 b(vidimo)e(da)j(deriv)-5 b(acija)31 b(impulsa)f(p)s(o)i Fm(x)h Ft(is)m(\024)-46 b(ceza)m(v)-5 b(a:)1184 3656 y Fm(@)1235 3671 y Fi(x)1280 3656 y Fm(\031)t Ft(\()p Fu(r)p Ft(\))p Fp(j)1489 3671 y Fi(x)p Fr(=0)1650 3656 y Ft(=)27 b Fp(\000)1878 3588 y Fm(L)p 1867 3632 89 4 v 1867 3724 a(N)1976 3588 y(@)2027 3603 y Fi(x)2071 3588 y Fm(\032)2121 3603 y Fr(0)2161 3588 y Ft(\()p Fm(x)p Ft(\))p 1976 3632 317 4 v 2024 3724 a Fm(\032)2074 3739 y Fr(0)2113 3724 y Ft(\()p Fm(x)p Ft(\))2302 3506 y Fj(\014)2302 3556 y(\014)2302 3606 y(\014)2302 3656 y(\014)2302 3705 y(\014)2330 3759 y Fi(x)p Fr(=0)2486 3656 y Ft(~)-54 b Fm(\031)s Ft(\()p Fm(y)t Ft(\))27 b(=)h(0)p Fm(:)726 b Ft(\(4.5\))257 3909 y(Kona)m(\024)-46 b(cno)29 b(imamo)d (hamiltonijan)f(izra)m(\024)-46 b(zen)28 b(p)s(omo)m(\023)-46 b(cu)28 b(jedno)s(dimenzijsk)m(og)g(p)s(olja)36 b(~)-58 b Fm(\032)p Ft(\()p Fm(y)t Ft(\))28 b(i)g(njem)m(u)257 4089 y(k)-5 b(anonski)33 b(k)m(onjugiranog)f(impulsa)j(~)-54 b Fm(\031)t Ft(\()p Fm(y)t Ft(\))350 4361 y Fm(H)35 b Ft(=)615 4294 y Fm(L)p 580 4338 138 4 v 580 4430 a Ft(2)p Fm(N)744 4244 y Fj(Z)843 4361 y Fm(dy)12 b Ft(~)-57 b Fm(\032)p Ft(\()p Fm(y)t Ft(\))1141 4215 y Fj( )1215 4294 y Fm(@)10 b Ft(~)-54 b Fm(\031)p 1215 4338 116 4 v 1219 4430 a(@)5 b(y)1341 4215 y Fj(!)1406 4238 y Fr(2)1468 4361 y Ft(+)1589 4294 y Fm(N)p 1576 4338 V 1576 4430 a Ft(2)p Fm(L)1718 4244 y Fj(Z)1817 4361 y Fm(dy)12 b Ft(~)-57 b Fm(\032)o Ft(\()p Fm(y)t Ft(\))2114 4215 y Fj( )2189 4294 y Ft(1)p 2189 4338 49 4 v 2189 4430 a(2)2283 4294 y Fm(@)p 2257 4338 109 4 v 2257 4430 a(@)5 b(y)2392 4361 y Ft(ln)25 b(~)-58 b Fm(\032)p Ft(\()p Fm(y)t Ft(\))21 b(+)2797 4294 y Fm(N)10 b Fp(j)p Fm(\025)p Fp(j)p 2797 4338 201 4 v 2865 4430 a Fm(L)3008 4361 y Fp(\000)3007 4244 y Fj(Z)3091 4361 y Fm(dy)3194 4320 y Fl(0)3296 4294 y Ft(~)-58 b Fm(\032)p Ft(\()p Fm(y)3427 4258 y Fl(0)3450 4294 y Ft(\))p 3226 4338 324 4 v 3226 4430 a(\()p Fm(y)25 b Fp(\000)e Fm(y)3489 4401 y Fl(0)3511 4430 y Ft(\))3559 4215 y Fj(!)3625 4238 y Fr(2)3681 4361 y Fm(:)3600 4542 y Ft(\(4.6\))257 4723 y(T)-8 b(o)41 b(je)g(hamiltonijan)36 b(Calogero)m(v)m(og)k(mo)s(del.)66 b(Jo)-5 b(\024)-44 b(s)38 b(\023)-46 b(cemo)40 b(resk)-5 b(alirati)38 b(p)s(olje)48 b(~)-58 b Fm(\032)q Ft(\()p Fm(y)t Ft(\))40 b Fp(!)h Fm(c\032)p Ft(\()p Fm(y)t Ft(\))f(i)257 4903 y(impuls)31 b(~)-54 b Fm(\031)s Ft(\()p Fm(y)t Ft(\))27 b Fp(!)g Fm(\031)t Ft(\()p Fm(y)t Ft(\))p Fm(=c)p Ft(,)g(te)g(usp)s(osta)m(viti) g(pun)m(u)h(k)m(oresp)s(ondenciju)g(s)f(hamiltonijanom)22 b(\(2.16\))283 5183 y Fm(H)36 b Ft(=)545 5116 y Fm(L)p 513 5160 131 4 v 513 5252 a(cN)670 5009 y Fj(8)670 5084 y(<)670 5233 y(:)754 5116 y Ft(1)p 754 5160 49 4 v 754 5252 a(2)829 5066 y Fj(Z)929 5183 y Fm(dy)t(\032)p Ft(\()p Fm(y)t Ft(\))1227 5037 y Fj( )1300 5116 y Fm(@)5 b(\031)p 1300 5160 116 4 v 1304 5252 a(@)g(y)1426 5037 y Fj(!)1492 5060 y Fr(2)1553 5183 y Ft(+)1661 5116 y(1)p 1661 5160 49 4 v 1661 5252 a(2)1737 5066 y Fj(Z)1836 5183 y Fm(dy)t(\032)p Ft(\()p Fm(y)t Ft(\))2134 5037 y Fj(")2191 5116 y Fm(\025)2248 5131 y Fi(c)2304 5116 y Fp(\000)23 b Ft(1)p 2191 5160 263 4 v 2297 5252 a(2)2498 5116 y Fm(@)p 2473 5160 109 4 v 2473 5252 a(@)5 b(y)2607 5183 y Ft(ln)16 b Fm(\032)p Ft(\()p Fm(y)t Ft(\))22 b(+)g Fm(\025)3060 5198 y Fi(c)3094 5183 y Fp(\000)3093 5066 y Fj(Z)3177 5183 y Fm(dy)3280 5142 y Fl(0)3335 5116 y Fm(\032)p Ft(\()p Fm(y)3475 5080 y Fl(0)3498 5116 y Ft(\))p 3312 5160 248 4 v 3312 5252 a Fm(y)j Fp(\000)e Fm(y)3537 5223 y Fl(0)3569 5037 y Fj(#)3618 5060 y Fr(2)3657 5009 y Fj(9)3657 5084 y(=)3657 5233 y(;)3748 5183 y Fm(:)3600 5391 y Ft(\(4.7\))p eop %%Page: 38 41 38 40 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(38)257 294 y(P)m(osto)5 b(ji)22 b(v)m(eza)h(izmed)p 1000 241 31 4 v(u)e(k)m(onstan)m(te)i(in)m(terak)m(cije)f(u)g(Jac)m(kiw-Pi)f(mo) s(delu)g Fp(j)p Fm(\025)p Fp(j)p Ft(,)i(statisti)m(\024)-46 b(ck)m(og)21 b(parame-)257 474 y(tra)33 b(u)f(Calogero)m(v)m(om)g(mo)s (delu)f Fm(\025)1485 489 y Fi(c)1552 474 y Ft(i)h(parametra)f Fm(c)p Ft(:)1393 669 y Fm(N)p 1393 713 89 4 v 1404 804 a(L)1491 736 y(c)d Ft(=)f Fm(\025)1721 751 y Fi(c)1778 736 y Fp(\000)c Ft(1)k(and)h Fm(\025)2206 669 y(N)2294 633 y Fr(2)2334 669 y Fm(c)2376 633 y Fr(2)p 2206 713 210 4 v 2258 804 a Fm(L)2324 776 y Fr(2)2453 736 y Ft(=)g Fm(\025)2614 751 y Fi(c)2648 736 y Fm(:)925 b Ft(\(4.8\))257 998 y(P)m(arametar)42 b Fm(c)h Ft(nije)f(slob)s(o)s(dan,)i(v)m(e)m (\023)-46 b(c)43 b(je)g(o)s(dred)p 1981 945 31 4 v(en)g(relacijom)d (normiranja)g(\(3.10\))i(gusto)m(\023)-46 b(ce)43 b(u)257 1178 y(Jac)m(kiw-Pi)32 b(mo)s(delu,)g(te)g(zah)m(tjev)m(om)1704 1323 y Fj(Z)1804 1440 y Fm(dy)t(\032)p Ft(\()p Fm(y)t Ft(\))26 b(=)h Fm(N)2292 1455 y Fi(c)2327 1440 y Fm(;)257 1702 y Ft(gdje)37 b(je)f Fm(N)657 1717 y Fi(c)728 1702 y Ft(bro)5 b(j)33 b(\024)-46 b(cestica)37 b(u)f(Calogero)m(v)m(om)f(mo) s(delu,)c(\024)-44 b(sto)36 b(nam)g(da)5 b(je)36 b Fm(c)e Ft(=)g Fm(L=)-5 b(N)3284 1717 y Fi(c)3318 1702 y Ft(.)55 b(Kona)m(\024)-46 b(cno,)257 1882 y(k)m(om)m(binacijom)20 b(gornjih)g(relacija)g(dobiv)-5 b(amo)20 b(v)m(ezu)k(med)p 2307 1830 V(u)d(statisti)m(\024)-46 b(ckim)20 b(parametrima)f(u)j(mo)s (d-)257 2063 y(elima:)1623 2244 y Fp(j)p Fm(\025)p Fp(j)1753 2119 y Fj(\014)1752 2169 y(\014)1752 2219 y(\014)1752 2268 y(\014)1801 2176 y Fm(N)p 1789 2220 113 4 v 1789 2312 a(N)1867 2327 y Fi(c)1912 2119 y Fj(\014)1912 2169 y(\014)1912 2219 y(\014)1912 2268 y(\014)1967 2244 y Ft(=)2194 2176 y Fm(\025)2251 2191 y Fi(c)p 2081 2220 318 4 v 2081 2312 a Fp(j)p Fm(\025)2166 2327 y Fi(c)2222 2312 y Fp(\000)h Ft(1)p Fp(j)2408 2244 y Fm(:)1165 b Ft(\(4.9\))257 2470 y(Sv)m(o)5 b(jstv)-5 b(a)34 b(o)m(v)m(e)g(relacije) d(k)m(omen)m(tirat)e(\023)-46 b(cemo)32 b(malo)f(k)-5 b(asnije,)32 b(u)h(o)m(v)m(om)f(o)s(djeljku.)404 2651 y(Rezultat)k(rada)g([32])g(je)h(vrlo)f(zanimljiv,)f(ali)f(je)j(zasno)m (v)-5 b(an)38 b(na)e(pretp)s(osta)m(v)m(ci)h(\(4.1\),)h(k)m(o)5 b(ju)257 2831 y(na)m(\024)-46 b(zalost)38 b(ne)h(mo)m(\024)-46 b(zemo)37 b(dok)-5 b(azati,)39 b(bar)g(ne)g(direktno.)61 b(Zato)37 b(smo)h(u)h(sljede)m(\023)-46 b(cem)39 b(k)m(oraku)g([11])257 3012 y(razmotrili)27 b(isti)i(problem,)h(u)h(nisk)m(o)s(energijsk)m(om) f(pribli)m(\024)-46 b(zenju,)30 b(i)f(upra)m(v)m(o)j(ta)e(istra)m(\024) -46 b(ziv)-5 b(anja)26 b(\024)-46 b(cine)257 3193 y(ok)m(osnicu)34 b(o)m(v)m(e)f(disertacije.)404 3373 y(U)21 b(drugom)g(p)s(ogla)m(vlju)f (smo)h(ukratk)m(o)i(izlo)m(\024)-46 b(zili)18 b(gla)m(vna)j(sv)m(o)5 b(jstv)-5 b(a)23 b(Calogero-Sutherlando)m(v)m(og)257 3554 y(mo)s(dela)39 b(u)h(k)m(olektivno)5 b(j)41 b(form)m(ulaciji,)d (te)j(smo)f(na)-5 b(\024)-44 b(sli)39 b(disp)s(erzivn)m(u)h(relaciju)f (\(2.75\))h(za)g(male)257 3734 y(kv)-5 b(an)m(tne)49 b(oscilacije)c(ok)m(o)i(k)m(onstan)m(tnog)h(rje)-5 b(\024)-44 b(senja.)88 b(U)47 b(tre)m(\023)-46 b(cem)47 b(p)s(ogla)m(vlju)f(smo)g (prou)m(\024)-46 b(ca)m(v)-5 b(ali)257 3915 y(Jac)m(kiw-Pi)45 b(mo)s(del,)i(gla)m(vna)e(sv)m(o)5 b(jstv)-5 b(a,)50 b(solitonsk)-5 b(a)44 b(rje)-5 b(\024)-44 b(senja,)50 b(te)45 b(k)m(ona)m(\024)-46 b(cno,)50 b(sp)s(ektar)c(malih)257 4095 y(oscilacija)39 b(ok)m(o)j(to)m(\024)-46 b(cno)41 b(o)s(dred)p 1349 4043 31 4 v(enog)h(rje)-5 b(\024)-44 b(senja.)70 b(Usp)s(oredimo)41 b(sp)s(ektar)h(malih)c(oscilacija)h(ok)m (o)257 4276 y(osno)m(vnog)34 b(stanja)e(u)h(Calogero-Sutherlando)m(v)m (om)e(mo)s(delu)g(i)h(u)g(Jac)m(kiw-Pi)g(mo)s(delu:)922 4538 y(Sutherlando)m(v)58 b(mo)s(del)26 b(:)166 b Fm(!)2086 4497 y Fi(s)2082 4562 y(n)2156 4538 y Ft(=)2288 4470 y(1)p 2270 4514 87 4 v 2270 4606 a Fm(r)2317 4572 y Fr(2)2314 4628 y(0)2382 4392 y Fj( )2448 4538 y Fp(\000)2535 4470 y Fm(\025)2592 4485 y Fi(s)2651 4470 y Fp(\000)23 b Ft(1)p 2535 4514 265 4 v 2643 4606 a(2)2810 4538 y Fm(n)2868 4497 y Fr(2)2930 4538 y Ft(+)3038 4470 y Fm(N)3116 4485 y Fi(s)3152 4470 y Fm(\025)3209 4485 y Fi(s)p 3038 4514 209 4 v 3117 4606 a Ft(2)3256 4538 y Fp(j)p Fm(n)p Fp(j)3370 4392 y Fj(!)3452 4538 y Fm(;)72 b Ft(\(2.75\))1037 4743 y(Jac)m(kiw)24 b Fp(\000)f Ft(Pi)54 b(mo)s(del)562 4949 y(\(sferno)23 b Fp(\000)g Ft(simetri)m(\024)-46 b(c)n(no)28 b(rje)-5 b(\024)-44 b(senje\))29 b(:)166 b Fm(!)2086 4908 y Fi(j)t(p)2082 4973 y(n)2185 4949 y Ft(=)2317 4881 y(1)p 2298 4925 87 4 v 2298 5017 a Fm(r)2345 4983 y Fr(2)2342 5039 y(0)2411 4803 y Fj( )2477 4949 y Ft(2)p Fm(n)2584 4908 y Fr(2)2645 4949 y Ft(+)22 b Fp(j)p Fm(n)p Fp(j)2867 4881 y Fm(N)2945 4896 y Fi(j)t(p)3017 4881 y Fp(j)p Fm(\025)3102 4896 y Fi(j)t(p)3174 4881 y Fp(j)p 2867 4925 335 4 v 3010 5017 a Ft(2)3211 4803 y Fj(!)3294 4949 y Fm(:)230 b Ft(\(3.49\))338 5210 y(V)-8 b(eli)m(\024)-46 b(cine)39 b Fm(\025)i Ft(i)e Fm(N)51 b Ft(s)41 b(indeksom)f Fm(s)h Ft(o)s(dnose)f(se)i(na)e(statisti)m(\024)-46 b(cki)39 b(parametar)h(i)f(bro)5 b(j)38 b(\024)-46 b(cestica)40 b(u)257 5391 y(Sutherlando)m(v)m(om)h(mo)s(delu,)g(dok)f(one)h(s)g (indeksom)f Fm(j)6 b(p)40 b Ft(ozna)m(\024)-46 b(ca)m(v)-5 b(a)5 b(ju)41 b(iste)f(parametre,)i(ali)c(u)p eop %%Page: 39 42 39 41 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(39)257 294 y(Jac)m(kiw-Pi)27 b(mo)s(delu.)40 b(Vidimo)24 b(da)j(su)g(izrazi)f (vrlo)g(sli)m(\024)-46 b(cni.)40 b(Disp)s(erzion)m(u)26 b(relaciju)f(za)i(Jac)m(kiw-Pi)257 474 y(mo)s(del)k(mo)m(\024)-46 b(zemo)32 b(resk)-5 b(alirati)1728 655 y Fm(!)1793 614 y Fi(j)t(p)1789 680 y(n)1892 655 y Fp(!)2069 587 y Ft(4)p Fm(!)2183 551 y Fi(j)t(p)2179 612 y(n)p 2029 632 265 4 v 2029 723 a Ft(1)22 b Fp(\000)h Fm(\025)2257 738 y Fi(s)2303 655 y Fm(;)257 889 y Ft(i)34 b(dobiv)-5 b(amo)33 b(disp)s(erzijsku)i(relaciju)e(iden)m(ti)m(\024)-46 b(cn)m(u)35 b(ono)5 b(j)35 b(za)g(Sutherlando)m(v)g(mo)s(del,)f(uk)m(olik)m(o)g (za-)257 1070 y(h)m(tjev)-5 b(amo)41 b(da)g(su)h(bro)5 b(j)39 b(\024)-46 b(cestica)41 b(i)f(statisti)m(\024)-46 b(cki)40 b(parametar)h(u)g(jednom)g(i)f(u)i(drugom)e(mo)s(delu)257 1251 y(v)m(ezani)33 b(relacijom:)1641 1431 y Fm(N)1719 1446 y Fi(j)t(p)1791 1431 y Fp(j)p Fm(\025)1876 1446 y Fi(j)t(p)1947 1431 y Fp(j)28 b Ft(=)2120 1364 y(4)p Fm(N)2247 1379 y Fi(s)2283 1364 y Fm(\025)2340 1379 y Fi(s)p 2116 1408 V 2116 1499 a Ft(1)22 b Fp(\000)h Fm(\025)2344 1514 y Fi(s)2390 1431 y Fm(:)1134 b Ft(\(4.10\))268 1640 y(\024)257 1666 y(Cini)26 b(se)j(priro)s(dnim)24 b(da)k(je)f(dinami)m (\024)-46 b(ck)-5 b(a)25 b(dimenzijsk)-5 b(a)26 b(reduk)m(cija)i(pra)m (\023)-46 b(cena)28 b(statisti)m(\024)-46 b(ck)m(om)26 b(trans-)257 1846 y(m)m(utacijom,)33 b(ali)f(ono)d(\024)-44 b(sto)34 b(o)m(vu)h(relciju)e(izdv)-5 b(a)5 b(ja)34 b(jest)e(\024)-46 b(cinjenica)33 b(da)h(je)h(relacija)d(\(4.10\))i(in)m(v)-5 b(ari-)257 2027 y(jan)m(tna)33 b(na)f(slijede)m(\023)-46 b(cu)33 b(transformaciju:)1515 2307 y Fm(\025)1572 2322 y Fi(s)1637 2307 y Fp(!)1796 2240 y Ft(1)p 1774 2284 94 4 v 1774 2375 a Fm(\025)1831 2390 y Fi(s)1905 2307 y Ft(i)27 b Fm(N)2038 2322 y Fi(s)2102 2307 y Fp(!)h(\000)p Fm(\025)2364 2322 y Fi(s)2401 2307 y Fm(N)2479 2322 y Fi(s)2516 2307 y Fm(:)1008 b Ft(\(4.11\))257 2587 y(Otprije)28 b(je)h(p)s(oznato)f(da)h(je)g(Calogero-Sutherlando)m(v)f(mo)s(del)f(in) m(v)-5 b(arijan)m(tan)27 b([33])h(na)h(tu)g(trans-)257 2768 y(formaciju)d("dualnosti".)40 b(Autori)27 b(rada)g([34])h(su)g (isk)m(oristili)c(tu)k(dualnost)g(da)f(bi)g(izra)m(\024)-46 b(cunali)26 b(k)m(o-)257 2948 y(relacijsk)m(e)f(funk)m(cije)g(gusto)m (\023)-46 b(ce)25 b(za)g(statisti)m(\024)-46 b(ck)m(e)25 b(parametre)f Fm(\025)2450 2963 y Fi(s)2511 2948 y Ft(i)g(1)p Fm(=\025)2718 2963 y Fi(s)2754 2948 y Ft(,)d(\024)-44 b(sto)25 b(je)g(k)-5 b(asnije)24 b(p)s(otvrd)p 3619 2896 31 4 v(eno)257 3129 y([14])36 b(k)m(ori)-5 b(\024)-44 b(stenjem)35 b(nekih)h(sv)m(o)5 b(jsta)m(v)-5 b(a)37 b(egzaktnog)f(rje)-5 b(\024)-44 b(senja)36 b(\(tj.)52 b(Jac)m(k)m(o)m(vih)37 b(p)s(olinoma\).)49 b(T)-8 b(o)36 b(je)257 3310 y(lijep)41 b(primjer)g(p)s(o)5 b(jma)40 b(dualnosti)h(tj.)72 b(v)m(eze)44 b(izmed)p 2183 3257 V(u)d(p)s(erturbativnog)h(i)f(nep)s(erturbativnog)257 3490 y(limesa)30 b(\(ne)i(n)m(u)m(\024)-46 b(zno)33 b(iste\))f (teorije.)42 b(Kori)-5 b(\024)-44 b(stenjem)31 b(relacija)f(dualnosti)g (p)s(ok)-5 b(azano)32 b(je)f(da)h(su)g(p)s(et)257 3671 y(razli)m(\024)-46 b(citih)25 b(teorija)g(sup)s(erstruna)k(zapra)m(v)m (o)f(samo)f(razli)m(\024)-46 b(citi)24 b(limesi)g(op)m(\023)-46 b(cenitije)27 b(M-)g(teorije.)41 b(Ak)m(o)257 3851 y(malo)36 b(b)s(olje)g(p)s(ogledamo)f(relaciju)h(dualnosti)g(\(4.11\))h(i)f (relaciju)g(\(4.10\))h(vidimo)e(da)i Fm(N)10 b Ft(,)40 b(bro)5 b(j)255 4032 y(\024)-46 b(cestica)33 b(mo)m(\024)-46 b(ze)33 b(promijeniti)d(predznak)35 b(\(!\),)29 b(\024)-44 b(sto)33 b(se)h(ba)-5 b(\024)-44 b(s)34 b(ne)d(\024)-46 b(cini)32 b(\014zik)-5 b(alnim.)43 b(No,)34 b(sama)e(tran-)257 4212 y(sformacija)39 b(dualnosti)g(o)s(dnosi)h(se)i(na)e(p)s(obud)p 1977 4160 V(enja)h(u)g(Calogero-Sutherlando)m(v)m(om)e(mo)s(delu,)257 4393 y(tj.)45 b(na)33 b(kv)-5 b(azi)m(\024)-46 b(cestice)34 b(i)e(kv)-5 b(azi)g(\024)-44 b(supljine,)33 b(i)f(tu)h(je)g Fm(N)44 b Ft(samo)32 b(parametar)g(pa)h(o)g(tome)f(ne)i(moramo)257 4574 y(brin)m(uti.)80 b(Ina)m(\024)-46 b(ce,)48 b(istu)d(v)m(ezu)i(mo)m (\024)-46 b(zemo)43 b(dobiti)g(uk)m(olik)m(o)i(usp)s(oredimo)e(disp)s (erzion)m(u)i(relaciju)257 4754 y(\(2.51\))35 b(za)g(Calogero)m(v)f(mo) s(del)f(i)h(izraz)h(za)g(sp)s(ektar)h(malih)c(\015uktuacija)j(u)g(Jac)m (kiw-Pi)f(mo)s(delu)257 4935 y(\(3.54\),)e(ok)m(o)h("zidnog")f(rje)-5 b(\024)-44 b(senja)33 b(\(3.30\):)933 5215 y(Calogero)m(v)56 b(mo)s(del)26 b(:)56 b Fm(!)1845 5174 y Fi(c)1841 5239 y(n)1915 5215 y Ft(=)2019 5069 y Fj( )2084 5215 y Fp(\000)2171 5147 y Fm(\025)2228 5162 y Fi(c)2286 5147 y Fp(\000)22 b Ft(1)p 2171 5192 263 4 v 2279 5283 a(2)2444 5215 y Fm(n)2502 5174 y Fr(2)2564 5215 y Ft(+)g Fm(\025)2719 5230 y Fi(c)2754 5215 y Fm(\031)t(\032)2863 5174 y Fi(c)2863 5239 y Fr(0)2902 5215 y Fp(j)p Fm(n)p Fp(j)3016 5069 y Fj(!)3098 5215 y Fm(;)426 b Ft(\(2.51\))p eop %%Page: 40 43 40 42 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(40)473 474 y(Jac)m(kiw)24 b Fp(\000)e Ft(Pi)55 b(mo)s(del)26 b(\(zidno)i(rje)-5 b(\024)-44 b(senje\))28 b(:)56 b Fm(!)2145 433 y Fi(j)t(p)2141 499 y(n)2244 474 y Ft(=)2347 328 y Fj( )2423 407 y Ft(1)p 2423 451 49 4 v 2423 543 a(2)2482 474 y Fm(n)2540 433 y Fr(2)2602 474 y Ft(+)2710 407 y Fm(N)2788 422 y Fi(j)t(p)2860 407 y Fp(j)p Fm(\025)2945 422 y Fi(j)t(p)3016 407 y Fp(j)p Fm(\031)p 2710 451 394 4 v 2873 543 a(L)3113 474 y Fp(j)p Fm(n)p Fp(j)3227 328 y Fj(!)3309 474 y Fm(;)215 b Ft(\(3.55\))307 688 y(gdje)24 b(je)h Fm(\032)655 703 y Fr(0)720 688 y Ft(u)g(disp)s(erziono)5 b(j)24 b(relaciji)e(za)j(Calogero)m(v)f(mo)s(del)f(k)m(onstan)m(tno)j (rje)-5 b(\024)-44 b(senje,)28 b(normirano)257 869 y(\(u)j("kutiji")e (duljine)g Fm(L)p Ft(\))i(k)-5 b(ao)31 b Fm(\032)1416 884 y Fr(0)1483 869 y Ft(=)c Fm(N)1664 884 y Fi(c)1699 869 y Fm(=L)1814 884 y Fi(c)1849 869 y Ft(,)k(tak)m(o)g(da)g(zapra)m(v) m(o)g(ne)g(dobiv)-5 b(amo)29 b(relaciju)g(\(4.10\),)257 1050 y(v)m(e)m(\023)-46 b(c)1416 1109 y Fj(\022)1487 1163 y Fm(N)p 1487 1207 89 4 v 1498 1299 a(L)1586 1109 y Fj(\023)1647 1309 y Fi(j)t(p)1735 1230 y Fp(j)p Fm(\025)1820 1245 y Fi(j)t(p)1892 1230 y Fp(j)27 b Ft(=)2051 1109 y Fj(\022)2122 1163 y Fm(N)p 2122 1207 V 2133 1299 a(L)2220 1109 y Fj(\023)2282 1309 y Fi(c)2428 1163 y Fm(\025)2485 1178 y Fi(c)p 2343 1207 263 4 v 2343 1299 a Ft(1)22 b Fp(\000)g Fm(\025)2570 1314 y Fi(c)2615 1230 y Fm(;)909 b Ft(\(4.12\))257 1444 y(no)22 b Fm(L)g Ft(je)g(o)m(vdje)g(samo)f (parametar)g(normalizacije)e(ina)m(\024)-46 b(ce)21 b(ne\014zik)-5 b(alnih)20 b(\(div)m(ergen)m(tnih\))i(rje)-5 b(\024)-44 b(senja,)257 1625 y(pa)36 b(mo)m(\024)-46 b(zemo)34 b(o)s(dabrati)g(da) h(bude)h(isti)e(u)i(oba)f(slu)m(\024)-46 b(ca)5 b(ja.)52 b(Primje)m(\023)-46 b(cujemo)34 b(i)g(razli)m(\024)-46 b(cit)33 b(n)m(umeri)m(\024)-46 b(cki)257 1805 y(faktor)33 b(u)h(relacijama)c(\(4.10\))j(i)f(\(4.12\),)h(no)g(on)h(je)f(p)s (osljedica)f(razli)m(\024)-46 b(citih)30 b(n)m(umeri)m(\024)-46 b(ckih)33 b(faktora)257 1986 y(u)h(relacijama)e(\(2.71\))h(i)g (\(3.41\))g(i)g(mo)m(\024)-46 b(ze)34 b(se)h(izb)5 b(je)m(\023)-46 b(ci)33 b(rede\014nicijom)g(nekih)h(k)m(onstan)m(ti.)48 b(Vidimo)257 2167 y(da)43 b(relacija)d(\(4.12\))i(o)s(dgo)m(v)-5 b(ara)41 b(relaciji)f(\(4.9\);)47 b(u)42 b(slu)m(\024)-46 b(ca)5 b(ju)43 b(k)-5 b(ad)42 b(je)g Fm(\025)2872 2182 y Fi(c)2951 2167 y Fm(<)i Ft(1,)h(gore)d(na)m(v)m(edene)257 2347 y(relacije)34 b(su)h(iden)m(ti)m(\024)-46 b(cne,)36 b(a)e(u)h(slu)m(\024)-46 b(ca)5 b(ju)35 b(k)-5 b(ad)35 b(je)g Fm(\025)2022 2362 y Fi(c)2088 2347 y Fm(>)c Ft(1,)k(u)g (relaciji)e(\(4.9\))h(napra)m(vimo)f(transfor-)257 2528 y(maciju)26 b(dualnosti)g(\(4.11\))h(i)g(op)s(et)g(dobijemo)f(relaciju) g(\(4.12\).)41 b(Dakle,)28 b(mo)m(\024)-46 b(zemo)26 b(zaklju)m(\024)-46 b(citi)26 b(da)257 2708 y(smo)33 b(uspijeli,)e(mak)-5 b(ar)32 b(indirektno,)g(p)s(otvrditi)f(pretp)s (osta)m(vku)k(\(4.1\),)d(o)h(funk)m(cionalnom)e(obli-)257 2889 y(ku)37 b(malih)d(kv)-5 b(an)m(tnih)36 b(oscilacija)e(u)j(Jac)m (kiw-Pi)f(mo)s(delu,)f(te)i(na)f(dv)-5 b(a)36 b(neekviv)-5 b(alen)m(tna)37 b(na)m(\024)-46 b(cina)257 3069 y(izv)m(esti)33 b(relaciju)e(\(4.12\),)h(k)m(o)5 b(ja)33 b(oslik)-5 b(a)m(v)g(a)31 b(tip)h(v)m(eze)i(med)p 2291 3017 31 4 v(u)f(analiziranim)28 b(mo)s(delima.)404 3250 y(Zanimljiv)m(ost)18 b(o)m(v)m(e)23 b(dimenzijsk)m(e)f(reduk)m(cije)h(jest)f(i)f(u)h(tome)f(da)g(njen)h (rezultat)g(nije)f(Calogero)m(v)257 3431 y(i/ili)30 b(Sutherlando)m(v)k (mo)s(del,)d(v)m(e)m(\023)-46 b(c)35 b(za)e(sv)-5 b(aki)33 b(o)s(d)g(njih)g(dobijemo)e(ob)5 b(je)34 b(mogu)m(\023)-46 b(cnosti-)32 b(mo)s(del)f(sa)257 3611 y(statisti)m(\024)-46 b(ckim)32 b(parametrom)g Fm(\025)h Ft(i)g(bro)5 b(jem)31 b(\024)-46 b(cestica)34 b Fm(N)10 b Ft(,)34 b(te)g(ona)5 b(j)34 b(sa)g(statisti)m(\024)-46 b(ckim)31 b(parametrom)257 3792 y(1)p Fm(=\025)c Ft(i)e(bro)5 b(jem)24 b(\024)-46 b(cestica)27 b Fp(\000)p Fm(\025N)10 b Ft(.)42 b(Izgleda)27 b(k)-5 b(ao)26 b(da)h(smo)f(iz)g(vi)-5 b(\024)-44 b(se)27 b(dimenzije)f(dobili)e("ob)5 b(ja)-5 b(\024)-44 b(snjenje")257 3972 y(za)44 b(p)s(osto)5 b(janje)44 b(o)s(dred)p 1085 3920 V(ene)h(simetrije)d(u)i(ni)m(\024)-46 b(zedimenzijsk)m(om)43 b(mo)s(delu.)76 b(T)-8 b(e)j(\024)-44 b(sk)m(o)45 b(je)f(p)s(otvrditi) 257 4153 y(o)m(v)-5 b(akvu)32 b(pretp)s(osta)m(vku,)g(zapra)m(v)m(o)f (in)m(terpretaciju)e(dobiv)m(enih)h(rezultata,)g(ali)e(sv)-5 b(ak)g(ak)m(o)31 b(je)f(vrlo)257 4334 y(in)m(trigan)m(tno,)f(i)f(u)i (sv)-5 b(ak)m(om)29 b(slu)m(\024)-46 b(cju)29 b(p)s(otpuno)g(u)h (skladu)f(s)h(motivima)c(k)m(o)5 b(ji)29 b(sto)5 b(je)30 b(iza)f(k)m(ori)-5 b(\024)-44 b(stenja)257 4514 y(dimenzijsk)m(e)33 b(reduk)m(cije)g(pri)f(analizi)e(o)s(dred)p 1862 4462 V(enih)j(\014zik)-5 b(alnih)30 b(susta)m(v)-5 b(a.)257 4931 y Fk(4.2)161 b(Kv)-9 b(an)l(tna)54 b(statistik)-9 b(a)257 5210 y Ft(Zanimljiv)m(o)40 b(je)k(i)e(pitanje)h(statistik)-5 b(a)42 b(u)h(mo)s(delima.)73 b(Naime,)45 b(u)e(jedno)5 b(j)44 b(i)f(dvije)g(prostorne)257 5391 y(dimenzije,)g(sam)e(k)m (oncept)i(statistik)m(e)e(je)g(suptilniji)e(nego)i(u)h(uobi)m(\024)-46 b(ca)5 b(jene)42 b(tri)e(prostorne)i(di-)p eop %%Page: 41 44 41 43 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(41)257 294 y(menzije.)42 b(U)30 b(ta)g(dv)-5 b(a)30 b(slu)m(\024)-46 b(ca)5 b(ja)29 b(mogu)m(\023)-46 b(ce)30 b(je)g(de\014nirati)e("in)m (termedijarn)m(u")h(statistiku,)h(o)s(dnosno)257 474 y(statistiku)i(k)m(o)5 b(ja)33 b(in)m(terp)s(olira)d(izmed)p 1595 422 31 4 v(u)i(b)s(ozonsk)m(og)i(i)d(fermionsk)m(og)h(slu)m(\024) -46 b(ca)5 b(ja.)404 655 y(Lak)m(o)28 b(se)h(mo)m(\024)-46 b(zemo)27 b(uvjeriti)g(da)h(se)g(spin)g(u)h(dvije)e(prostorne)i (dimenzije)e(bitno)g(razikuje)h(o)s(d)257 835 y(spina)36 b(u)g(tri)e(ili)f(vi)-5 b(\024)-44 b(se)37 b(prostornih)e(dimenzija.)51 b(Naime,)35 b(algebra)g(angularnog)f(impulsa)g(spina)257 1016 y(je)f(u)g(tri)e(dimenzije)h(nek)m(om)m(utativna)1346 1296 y([)p Fm(S)1433 1311 y Fi(i)1461 1296 y Fm(;)17 b(S)1565 1311 y Fi(j)1601 1296 y Ft(])28 b(=)f Fm(i\017)1831 1311 y Fi(ij)t(k)1931 1296 y Fm(S)1991 1311 y Fi(k)2034 1296 y Fm(;)44 b(i;)17 b(j;)g(k)31 b Ft(=)d(1)p Fm(;)17 b Ft(2)p Fm(;)g Ft(3)p Fm(;)257 1576 y Ft(dok)29 b(u)g(dvije)g (dimenzije)e(imamo)f(trivijalno)f(k)m(om)m(utativn)m(u)k(algebru,)g (jer)g(p)s(osto)5 b(ji)27 b(samo)h(jedan)257 1757 y(generator.)57 b(P)m(osljedica)37 b(nek)m(om)m(utativnosti)g(algebre)f(jest)i(da)f(iz) f(zah)m(tjev)-5 b(a)38 b(za)f(p)s(ozitivno)-5 b(\024)-44 b(s)m(\023)e(cu)257 1938 y(norme)37 b(vlastitih)e(stanja)i(slijedi)f (da)h(vlastite)f(vrijednosti)g(spinsk)m(og)i(angularnog)e(momen)m(ta) 257 2118 y(mora)5 b(ju)34 b(biti)f(cijeli)f(ili)g(p)s(olucijelobro)5 b(jni)32 b(vi)-5 b(\024)-44 b(sekratnici)34 b(\026)-50 b Fm(h)p Ft(.)49 b(U)35 b(dvije)g(prostorne)g(dimenzije)e(ne)257 2299 y(p)s(osto)5 b(je)29 b(nik)-5 b(akvi)27 b(uvjeti)h(na)g(vlastite)f (vrijednosti)g(spinsk)m(og)i(angularnog)e(momen)m(ta,)g(pa)h(tak)m(o) 257 2479 y(on)c(mo)m(\024)-46 b(ze)23 b(p)s(oprimiti)c(bilo)j(k)m(o)5 b(ji)23 b(vrijednost.)41 b(U)23 b(relativisti)m(\024)-46 b(ck)m(o)5 b(j)22 b(kv)-5 b(an)m(tno)5 b(j)24 b(teoriji)e(p)s(olja)f(p) s(osto)5 b(ji)257 2660 y(v)m(eza)38 b(izmed)p 693 2608 V(u)e(spina)e(\024)-46 b(cestica)37 b(i)f(njiho)m(v)m(e)h(statistik)m (e)f(\(spin-statistik)-5 b(a)35 b(teorem)h([35]\),)i(pa)e(tak)m(o)257 2840 y(mo)m(\024)-46 b(zemo)27 b(zaklju)m(\024)-46 b(citi)26 b(da)f(\024)-46 b(cestice)28 b(u)g(dvije)g(dimenzije)e(mogu)h(imati)e (bilo)h(k)m(o)5 b(ju-)28 b(in)m(termedijarn)m(u)257 3021 y(statistiku.)45 b(U)34 b(jedno)5 b(j)33 b(prostorno)5 b(j)34 b(dimenziji)c(spin)j(nije)g(de\014niran,)g(pa)h(se)g(p)s(o)5 b(jam)32 b(statistik)m(e)257 3202 y(mora)g(de\014nirati)f(druga)m(\024) -46 b(cije-)31 b(ne)-5 b(\024)-44 b(sto)34 b(vi)-5 b(\024)-44 b(se)33 b(o)f(tome)g(k)-5 b(asnije.)404 3382 y(Uobi)m(\024)-46 b(ca)5 b(jena)51 b(de\014nicija)g(kv)-5 b(an)m(tne)52 b(statistik)m(e)g(o)s(dnosi)e(se)j(na)e(fazu)g(k)m(o)5 b(ju)53 b(dobije)e(v)-5 b(alna)257 3563 y(funk)m(cije)38 b(k)-5 b(ad)37 b(zamijenimo)d(dvije)j(iden)m(ti)m(\024)-46 b(cne)34 b(\024)-46 b(cestice,)39 b(no)e(ispra)m(vno)h(bi)e(bilo)f(re)m (\023)-46 b(ci)37 b(da)g(se)h(radi)257 3743 y(o)33 b(fazi)f(k)m(o)5 b(ja)33 b(se)h(ja)m(vlja)e(k)-5 b(ad)33 b(dvije)d(\024)-46 b(cestice)33 b Fq(adijab)-5 b(atski)32 b Ft(transp)s(ortiramo)e(da)j (bi)f(ih)g(zamijenili.)257 3924 y(U)43 b(tri)f(ili)e(vi)-5 b(\024)-44 b(se)43 b(dimenzija)e(gornje)i(de\014nicije)f(su)i(iden)m (ti)m(\024)-46 b(cne,)45 b(no)e(u)g(ni)m(\024)-46 b(zim)41 b(dimenzijama)f(to)257 4104 y(vi)-5 b(\024)-44 b(se)42 b(nije)f(tak)m(o.)70 b(T)-8 b(o)42 b(je)f(v)m(ezano)i(za)38 b(\024)-46 b(cinjenicu)41 b(da)g(pra)m(vi)h(k)m(on\014guracijski)f (prostor)g(sistema)257 4285 y(iden)m(ti)m(\024)-46 b(cnih)40 b(\024)-46 b(cestica,)45 b(tj.)75 b(prostor)43 b(u)g(k)m(ome)g(su)h (iden)m(ti\014cirane)e(to)m(\024)-46 b(ck)m(e)44 b(k)m(o)5 b(je)44 b(o)s(dgo)m(v)-5 b(ara)5 b(ju)42 b(ra-)257 4466 y(zli)m(\024)-46 b(citom)34 b(ozna)m(\024)-46 b(ca)m(v)-5 b(anju)35 b(\024)-46 b(cestica,)38 b(sadr)m(\024)-46 b(zi)37 b(singularne)f(to)m(\024)-46 b(ck)m(e.)58 b(T)-8 b(o)37 b(su)h(to)m(\024)-46 b(ck)m(e)38 b(gdje)f(se)h(p)s(olo)m(\024) -46 b(za)5 b(ji)257 4646 y(dviju)27 b(ili)d(vi)-5 b(\024)-44 b(se)24 b(\024)-46 b(cestica)27 b(p)s(o)s(dudara)5 b(ju.)41 b(T)-8 b(o)27 b(zna)m(\024)-46 b(ci)27 b(da)f(v)-5 b(alne)27 b(funk)m(cije)g(mogu)f(biti)f(vi)-5 b(\024)-44 b(sezna)m(\024)e(cne,)29 b(te)257 4827 y(k)-5 b(ad)28 b(\024)-46 b(cestica)29 b(pred)p 902 4774 V(e)i(put)f(p)s(o)g(zatv)m(oreno)5 b(j)31 b(krivulji)d(ok)m(o)i(singulariteta,)e(v)-5 b(alna)29 b(funk)m(cija)h(dobiv)-5 b(a)257 5007 y(netrivijalni)30 b(fazni)i(faktor.)404 5188 y(Razmotrimo)39 b(to)i(p)s(obli)m(\024)-46 b(ze.)71 b(Nek)-5 b(a)42 b(je)g(k)m(o\014guracijski)g(prostor)g(jedne)e (\024)-46 b(cestice)43 b Fm(X)8 b Ft(.)71 b(Kon-)257 5368 y(\014guracijski)37 b(prostor)h Fm(N)48 b Ft(iden)m(ti)m(\024)-46 b(cnih)34 b(\024)-46 b(cestica,)38 b(nije,)h(k)-5 b(ak)m(o)38 b(bi)f(to)g(naivno)g(p)s(omislili)32 b Fm(X)3532 5332 y Fi(N)3599 5368 y Ft(,)39 b(v)m(e)m(\023)-46 b(c)p eop %%Page: 42 45 42 44 bop 257 -89 a Fs(4.)44 b(DISKUSIJA)2801 b Ft(42)257 294 y Fm(X)346 258 y Fi(N)413 294 y Fm(=S)522 309 y Fi(N)589 294 y Ft(,)29 b(gdje)e(je)g Fm(S)1008 309 y Fi(N)1102 294 y Ft(diskretna,)i(k)m(ona)m(\024)-46 b(cna)27 b(grupa)g(dobiv)m (ena)g(p)s(erm)m(utacijama)e Fm(N)38 b Ft(iden)m(ti)m(\024)-46 b(cnih)255 474 y(\024)g(cestica.)41 b(Prostori)24 b Fm(X)1065 438 y Fi(N)1158 474 y Ft(i)g Fm(X)1299 438 y Fi(N)1366 474 y Fm(=S)1475 489 y Fi(N)1568 474 y Ft(su)i(lok)-5 b(alno)23 b(izomorfni,)h(osim)g(u)h(singularnim)e(to)m(\024)-46 b(ck)-5 b(ama,)26 b(no)257 655 y(globalno)32 b(su)i(bitno)f(razlikuju.) 45 b(Da)33 b(bismo)f(o)s(dredili)f(k)m(on\014guracijski)j(prostor)g Fm(N)44 b Ft(iden)m(ti)m(\024)-46 b(cnih)255 835 y(\024)g(cestica,)31 b(moramo)d(iz)i Fm(X)1165 799 y Fi(N)1232 835 y Fm(=S)1341 850 y Fi(N)1438 835 y Ft(isklju)m(\024)-46 b(citi)28 b(to)m(\024)-46 b(ck)m(e)32 b(u)f(k)m(o)5 b(jima)29 b(se)i(p)s(olo)m (\024)-46 b(za)5 b(ji)29 b(dviju)h(ili)d(vi)-5 b(\024)-44 b(se)29 b(\024)-46 b(cestica)257 1016 y(p)s(o)s(dudara)5 b(ju.)76 b(T)-8 b(ak)m(o)43 b(dobiv)-5 b(amo)42 b(prostor)h(sa)g (singularitetima,)f(te)h(v)-5 b(alna)42 b(funk)m(cija)i(dobiv)-5 b(a)257 1197 y(fazni)33 b(faktor)h(k)-5 b(ad)33 b(obid)p 1115 1144 31 4 v(emo)g(ok)m(o)h(singulariteta.)44 b(T)-8 b(a)5 b(j)35 b(obilazak)d(ok)m(o)i(singulariteta)d(\014zik)-5 b(alno)257 1377 y(o)s(dgo)m(v)g(ara)41 b(zamijeni)e(dviju)g(\024)-46 b(cestica,)38 b(\024)-44 b(sto)42 b(u)f(tri)g(prostorne)h(dimenzije)e (da)5 b(je)42 b(+1)f(za)g(b)s(ozone)257 1558 y(i)j Fp(\000)p Ft(1)g(za)h(fermione,)h(dok)f(su)g(u)g(dvije)f(dimenzije)f(mogu)m(\023) -46 b(ci)43 b(i)g(drugi)h(fazni)g(faktori.)78 b(P)m(osto-)257 1738 y(janje)27 b(singulariteta)e(u)i(bilo)f(k)m(o)5 b(jem,)28 b(pa)g(tak)m(o)f(i)f(u)h(k)m(on\014guracijsk)m(om,)i (prostoru)e(za)g(p)s(osljedicu)257 1919 y(ima)35 b(vi)-5 b(\024)-44 b(sestruku)39 b(p)s(o)m(v)m(ezanost)g(dv)m(o)s(dimenzijsk)m (og)d(prostora)h(i)f(samo)g(dv)m(ostruku)j(p)s(o)m(v)m(ezanost)257 2099 y(u)d(tri)f(prostorne)i(dimenzije.)52 b(Matemati)m(\024)-46 b(cki)35 b(re)m(\024)-46 b(ceno)36 b(prv)-5 b(a)36 b(klasa)g (homotopije)e Fm(\031)3326 2114 y Fr(1)3366 2099 y Ft(\()p Fm(X)3493 2063 y Fi(N)3560 2099 y Fm(=S)3669 2114 y Fi(N)3736 2099 y Ft(\),)257 2280 y(o)s(dnosno)f(grupa)f(k)m(o)5 b(ju)31 b(\024)-46 b(cine)32 b(klase)h(neekviv)-5 b(alen)m(tnih)33 b(krivulja,)e(je)1442 2559 y Fm(\031)1497 2574 y Fr(1)1537 2559 y Ft(\()p Fm(X)1664 2518 y Fi(N)1731 2559 y Fm(=S)1840 2574 y Fi(N)1907 2559 y Ft(\))48 b(=)27 b Fm(B)2170 2574 y Fi(N)2265 2559 y Ft(za)h Fm(d)g Ft(=)f(2)1993 2765 y(=)g Fm(S)2156 2780 y 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Fm(@)g(N)1906 558 y Fi(j)1981 474 y Ft(=)27 b Fp(\000)p Fm(g)2208 489 y Fi(ij)2269 474 y Fm(:)1255 b Ft(\(4.13\))257 709 y(Za)35 b(b)s(ozone,)h(bro)5 b(j)35 b(mogu)m(\023)-46 b(cih)34 b(\(slob)s(o)s(dnih\))f(jedno)m(\024)-46 b(cesti)m(\024)g (cnih)35 b(stanja)g(ne)h(o)m(visi)e(o)h(bro)5 b(ju)35 b Fm(N)3598 724 y Fi(j)3635 709 y Ft(,)h(pa)257 889 y(je)42 b Fm(g)419 904 y Fi(ij)523 889 y Ft(=)i(0.)71 b(Za)41 b(fermione,)j(bro)5 b(j)42 b(slob)s(o)s(dnih)e(jedno)m(\024)-46 b(cesti)m(\024)g(cnih)42 b(stanja)g(se)h(smanji)d(za)i(jedan)257 1070 y(sa)f(sv)-5 b(ak)m(om)40 b(do)s(danom)d(\024)-46 b(cesticom,)41 b(pa)f(je)h Fm(g)1907 1085 y Fi(ij)2008 1070 y Ft(=)f Fm(\016)2167 1085 y Fi(ij)2228 1070 y Ft(.)66 b(Gla)m(vna)40 b(razlik)-5 b(a)38 b(izmed)p 3200 1018 31 4 v(u)i(standarnog)257 1251 y(pristupa)28 b(statistici)f(i)g (Haldaneo)m(v)m(og)h(je)g(u)g(tome)23 b(\024)-44 b(sto)28 b(se)h(u)f(prv)m(om)g(pristupu)h(statistik)-5 b(a)26 b(o)s(dnosi)257 1431 y(na)k(realne,)g(to)m(\024)-46 b(ck)-5 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b(Zapra)m(v)m(o,)50 b(bilo)45 b(bi)g(b)s(olje)h(napisati) f(recimo)257 3905 y(relaciju)28 b(\(4.12\))h(u)g(obliku)f(k)m(o)5 b(ji)29 b(jasno)g(o)s(da)5 b(je)29 b(on)m(u)h Fq(klasi)n(\024)-47 b(cnu)27 b Ft(relaciju)h(dualnosti-)f(o)s(dnos)j(jak)m(og)257 4086 y(i)i(slab)s(og)f(v)m(ezanja:)1589 4266 y Fm(\024)d Ft(=)1776 4145 y Fj(\022)1870 4199 y Ft(1)p 1847 4243 94 4 v 1847 4335 a Fm(\025)1904 4350 y Fi(s)1973 4266 y Fp(\000)23 b Ft(1)2122 4145 y Fj(\023)2246 4199 y Fm(N)2324 4214 y Fi(j)t(p)p 2209 4243 223 4 v 2209 4335 a Ft(8)p Fm(\031)t(N)2395 4350 y Fi(s)2442 4266 y Fm(;)257 4501 y Ft(gdje)32 b(je)f Fm(\024)h Ft(k)m(onstan)m(ta)h(in)m(terak)m(cije)e (u)g(Chern-Simonso)m(v)m(o)5 b(j)32 b(teoriji.)42 b(Nadam)30 b(se)i(da)d(\023)-46 b(ce)32 b(budu)m(\023)-46 b(ca)257 4681 y(istra)m(\024)g(ziv)-5 b(anja)31 b(p)s(otvrditi)g(o)m(v)-5 b(a)32 b(razmi)-5 b(\024)-44 b(sljanja.)p eop %%Page: 46 49 46 48 bop 257 1082 a Fv(Do)6 b(datak)79 b(A)257 1622 y(Grupa)f(pletenica)257 2135 y Ft(Grupa)31 b(pletenica)e(o)s(d)i Fm(N)41 b Ft(niti)29 b(\()p Fm(B)1514 2150 y Fi(N)1581 2135 y Ft(\))h(je)h(b)s(esk)m(ona)m(\024)-46 b(cna)32 b(grupa)f(k)m(o)5 b(ja)31 b(ima)d Fm(N)h Fp(\000)19 b Ft(1)30 b(generatora)g Fm(\033)3760 2150 y Fi(I)257 2315 y Ft(\(1)e Fp(\024)g Fm(I)35 b Fp(\024)29 b Fm(N)j Fp(\000)23 b Ft(1\).)43 b(Ti)32 b(generatori)g(zado)m(v)m(olja)m(v)-5 b(a)5 b(ju)32 b(sljede)m(\023)-46 b(ce)34 b(dvije)e(relacije:)1068 2596 y Fm(\033)1123 2611 y Fi(I)1163 2596 y Fm(\033)1218 2611 y Fi(I)5 b Fr(+1)1349 2596 y Fm(\033)1404 2611 y Fi(I)1472 2596 y Ft(=)27 b Fm(\033)1630 2611 y Fi(I)5 b Fr(+1)1761 2596 y Fm(\033)1816 2611 y Fi(I)1856 2596 y Fm(\033)1911 2611 y Fi(I)g Fr(+1)2070 2596 y Ft(za)27 b Fm(I)36 b Ft(=)27 b(1)p Fm(;)17 b Ft(2)p Fm(;)g(:)g(:)g(:)e(;)i(N)33 b Fp(\000)22 b Ft(2)586 b(\(A.1\))1454 2876 y Fm(\033)1509 2891 y Fi(I)1549 2876 y Fm(\033)1604 2891 y Fi(J)1681 2876 y Ft(=)28 b Fm(\033)1840 2891 y Fi(J)1889 2876 y Fm(\033)1944 2891 y Fi(I)2012 2876 y Ft(za)g Fp(j)p 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b(na)f(satu,)k(i)c(to)g(tak)m(o)h(da)f(ne)h(zah)m(v)-5 b(atimo)44 b(niti)257 4013 y(jedn)m(u)f(drugu)f(nit.)71 b(In)m(v)m(erzni)43 b(generator)f Fm(\033)1926 3972 y Fl(\000)p Fr(1)1922 4037 y Fi(I)2020 4013 y Ft(,)i(o)s(dgo)m(v)-5 b(ara)41 b(obrn)m(utom)h("kri)m(\024)-46 b(zanju")41 b(niti,)c(\024)-44 b(sto)257 4194 y(je)37 b(prik)-5 b(azano)35 b(na)i(slici)d(\(A1\).)55 b(Na)36 b(slijede)m(\023)-46 b(ce)37 b(dvije)f(slik)m(e)g(\(slik)m(e)g(\(A2\))g(i)g(\(A3\)\))g(prik) -5 b(azane)36 b(su)257 4374 y(relacije)c(\(A.1\))h(i)f(\(A.2\).)44 b(Iz)34 b(prilo)m(\024)-46 b(zenih)31 b(slik)-5 b(a,)32 b(te)h(gore)g(na)m(v)m(edenih)h(sv)m(o)5 b(jsta)m(v)-5 b(a,)35 b(lak)m(o)d(mo)m(\024)-46 b(zemo)257 4555 y(zaklju)m(\024)g (citi)39 b(da)i(je)g(grupa)g(pletenica)f(puno)i(b)s(ogatija)c(o)s(d)j (grup)s(e)g(p)s(erm)m(utacija.)67 b(Razmotrite)257 4735 y(dvije)33 b(putanja)f(prik)-5 b(azane)33 b(na)f(slici)f(\(A4\).)43 b(U)33 b(oba)f(prik)-5 b(azana)32 b(slu)m(\024)-46 b(ca)5 b(ja)32 b(nema)h(p)s(erm)m(utacije,)f(i)252 4916 y(\024)-44 b(sto)28 b(se)h(grup)s(e)f(p)s(erm)m(utacija)e(ti)m(\024)-46 b(ce,)29 b(oba)e(slu)m(\024)-46 b(ca)5 b(ja)28 b(pripada)5 b(ju)27 b(u)h(klasu)g(za)5 b(jedno)28 b(s)g(iden)m(titetom,)g(i)257 5097 y(grupa)i(p)s(erm)m(utacija)f(ne)i(razlikuje)e(te)i(putanje.)43 b(No,)31 b(te)f(dvije)g(putanje)h(su)g(razli)m(\024)-46 b(citi)27 b(elemen)m(ti)257 5277 y(grup)s(e)33 b(pletenica.)1980 5674 y(46)p eop %%Page: 47 50 47 49 bop 257 -89 a Fs(DOD)m(A)-8 b(T)g(AK)32 b(A.)66 b(GR)m(UP)-8 b(A)32 b(PLETENICA)1787 b Ft(47)p 404 2086 1654 4 v 404 904 V 520 2084 4 1182 v 756 2084 V 1701 2084 V 1937 2084 V 498 2202 a(1)187 b(2)306 b(I)154 b(I+1)194 b(N-1)129 b(N)p 1111 2084 4 473 v 1347 2084 V 1111 1375 V 1347 1375 V 1112 1613 4 4 v 1113 1611 V 1113 1610 V 1114 1608 V 1114 1606 V 1115 1605 V 1115 1603 V 1116 1602 V 1116 1600 V 1117 1598 V 1117 1597 V 1118 1595 V 1118 1594 V 1119 1592 V 1119 1591 V 1120 1589 V 1120 1588 V 1121 1586 V 1122 1585 V 1122 1583 V 1123 1582 V 1124 1580 V 1124 1579 V 1125 1578 V 1126 1576 V 1126 1575 V 1127 1573 V 1128 1572 V 1128 1571 V 1129 1569 V 1130 1568 V 1131 1567 V 1131 1565 V 1132 1564 V 1133 1563 V 1134 1561 V 1135 1560 V 1135 1559 V 1136 1558 V 1137 1556 V 1138 1555 V 1139 1554 V 1140 1553 V 1141 1551 V 1141 1550 V 1142 1549 V 1143 1548 V 1144 1547 V 1145 1546 V 1146 1544 V 1147 1543 V 1148 1542 V 1149 1541 V 1150 1540 V 1151 1539 V 1152 1538 V 1153 1537 V 1154 1536 V 1155 1535 V 1156 1534 V 1157 1533 V 1159 1532 V 1160 1531 V 1161 1530 V 1162 1529 V 1163 1528 V 1164 1527 V 1165 1526 V 1166 1525 V 1168 1524 V 1169 1523 V 1170 1522 V 1171 1521 V 1172 1521 V 1174 1520 V 1175 1519 V 1176 1518 V 1177 1517 V 1179 1516 V 1180 1516 V 1181 1515 V 1183 1514 V 1184 1513 V 1185 1513 V 1187 1512 V 1188 1511 V 1189 1510 V 1191 1510 V 1192 1509 V 1194 1508 V 1195 1508 V 1196 1507 V 1198 1506 V 1199 1506 V 1201 1505 V 1202 1504 V 1204 1504 V 1205 1503 V 1207 1503 V 1208 1502 V 1210 1501 V 1211 1501 V 1213 1500 V 1214 1500 V 1216 1499 V 1217 1499 V 1219 1498 V 1221 1498 V 1222 1497 V 1224 1497 V 1225 1496 V 1227 1496 V 1229 1495 V 1230 1495 V 1230 1495 V 1232 1495 V 1234 1494 V 1235 1494 V 1237 1493 V 1239 1493 V 1240 1492 V 1242 1492 V 1243 1491 V 1245 1491 V 1247 1490 V 1248 1490 V 1250 1489 V 1251 1489 V 1253 1488 V 1254 1487 V 1256 1487 V 1257 1486 V 1259 1486 V 1260 1485 V 1262 1484 V 1263 1484 V 1265 1483 V 1266 1482 V 1267 1482 V 1269 1481 V 1270 1480 V 1272 1480 V 1273 1479 V 1274 1478 V 1276 1477 V 1277 1477 V 1278 1476 V 1280 1475 V 1281 1474 V 1282 1474 V 1283 1473 V 1285 1472 V 1286 1471 V 1287 1470 V 1288 1469 V 1290 1469 V 1291 1468 V 1292 1467 V 1293 1466 V 1294 1465 V 1296 1464 V 1297 1463 V 1298 1462 V 1299 1461 V 1300 1460 V 1301 1459 V 1302 1458 V 1304 1457 V 1305 1456 V 1306 1455 V 1307 1454 V 1308 1453 V 1309 1452 V 1310 1451 V 1311 1450 V 1312 1449 V 1313 1448 V 1314 1447 V 1315 1445 V 1316 1444 V 1317 1443 V 1318 1442 V 1319 1441 V 1319 1440 V 1320 1439 V 1321 1437 V 1322 1436 V 1323 1435 V 1324 1434 V 1325 1432 V 1326 1431 V 1326 1430 V 1327 1429 V 1328 1427 V 1329 1426 V 1330 1425 V 1330 1423 V 1331 1422 V 1332 1421 V 1333 1419 V 1333 1418 V 1334 1417 V 1335 1415 V 1335 1414 V 1336 1412 V 1337 1411 V 1337 1410 V 1338 1408 V 1339 1407 V 1339 1405 V 1340 1404 V 1340 1402 V 1341 1401 V 1342 1399 V 1342 1398 V 1343 1396 V 1343 1395 V 1344 1393 V 1344 1391 V 1345 1390 V 1345 1388 V 1346 1387 V 1346 1385 V 1347 1383 V 1347 1382 V 1348 1380 V 1348 1379 V 1349 1377 V 1112 1377 V 1113 1379 V 1113 1380 V 1114 1382 V 1115 1383 V 1115 1385 V 1116 1387 V 1116 1388 V 1117 1390 V 1118 1391 V 1118 1393 V 1119 1394 V 1119 1396 V 1120 1397 V 1121 1399 V 1121 1400 V 1122 1401 V 1123 1403 V 1123 1404 V 1124 1406 V 1125 1407 V 1125 1408 V 1126 1410 V 1127 1411 V 1128 1412 V 1128 1413 V 1129 1415 V 1130 1416 V 1130 1417 V 1131 1418 V 1132 1420 V 1133 1421 V 1133 1422 V 1134 1423 V 1135 1424 V 1136 1425 V 1137 1426 V 1137 1427 V 1138 1428 V 1139 1429 V 1140 1430 V 1141 1432 V 1141 1432 V 1142 1433 V 1143 1434 V 1144 1435 V 1145 1436 V 1146 1437 V 1147 1438 V 1147 1439 V 1148 1440 V 1149 1441 V 1150 1441 V 1151 1442 V 1152 1443 V 1153 1444 V 1154 1445 V 1155 1445 V 1156 1446 V 1157 1447 V 1157 1447 V 1158 1448 V 1159 1449 V 1160 1449 V 1161 1450 V 1162 1451 V 1163 1451 V 1164 1452 V 1165 1452 V 1166 1453 V 1167 1454 V 1168 1454 V 1169 1455 V 1170 1455 V 1171 1456 V 1172 1456 V 1173 1456 V 1175 1457 V 1176 1457 V 1177 1458 V 1178 1458 V 1179 1458 V 1180 1459 V 1181 1459 V 1182 1459 V 1183 1460 V 1278 1530 V 1279 1531 V 1280 1531 V 1281 1531 V 1282 1532 V 1283 1532 V 1284 1532 V 1285 1533 V 1286 1533 V 1287 1534 V 1288 1534 V 1290 1534 V 1291 1535 V 1292 1535 V 1293 1536 V 1294 1536 V 1295 1537 V 1296 1538 V 1297 1538 V 1298 1539 V 1299 1539 V 1300 1540 V 1301 1540 V 1302 1541 V 1303 1542 V 1303 1542 V 1304 1543 V 1305 1544 V 1306 1545 V 1307 1545 V 1308 1546 V 1309 1547 V 1310 1548 V 1311 1548 V 1312 1549 V 1313 1550 V 1313 1551 V 1314 1552 V 1315 1553 V 1316 1554 V 1317 1555 V 1318 1556 V 1319 1557 V 1319 1557 V 1320 1558 V 1321 1559 V 1322 1560 V 1323 1562 V 1324 1563 V 1324 1564 V 1325 1565 V 1326 1566 V 1327 1567 V 1327 1568 V 1328 1569 V 1329 1570 V 1330 1572 V 1330 1573 V 1331 1574 V 1332 1575 V 1333 1577 V 1333 1578 V 1334 1579 V 1335 1580 V 1335 1582 V 1336 1583 V 1337 1584 V 1338 1586 V 1338 1587 V 1339 1589 V 1339 1590 V 1340 1591 V 1341 1593 V 1341 1594 V 1342 1596 V 1343 1597 V 1343 1599 V 1344 1600 V 1345 1602 V 1345 1603 V 1346 1605 V 1346 1607 V 1347 1608 V 1347 1610 V 1348 1611 V 1349 1613 V 853 1493 a Fb(r)22 b(r)g(r)542 b(r)22 b(r)g(r)p 2175 2086 1654 4 v 2175 904 V 2292 2084 4 1182 v 2528 2084 V 3473 2084 V 3709 2084 V 2270 2202 a Ft(1)187 b(2)305 b(I)154 b(I+1)195 b(N-1)128 b(N)p 2882 2084 4 473 v 3119 2084 V 2882 1375 V 3119 1375 V 2884 1613 4 4 v 2885 1611 V 2885 1610 V 2886 1608 V 2886 1607 V 2887 1605 V 2887 1603 V 2888 1602 V 2889 1600 V 2889 1599 V 2890 1597 V 2891 1596 V 2891 1594 V 2892 1593 V 2892 1591 V 2893 1590 V 2894 1589 V 2894 1587 V 2895 1586 V 2896 1584 V 2896 1583 V 2897 1582 V 2898 1580 V 2899 1579 V 2899 1578 V 2900 1577 V 2901 1575 V 2901 1574 V 2902 1573 V 2903 1572 V 2904 1570 V 2904 1569 V 2905 1568 V 2906 1567 V 2907 1566 V 2907 1565 V 2908 1564 V 2909 1563 V 2910 1562 V 2911 1560 V 2911 1559 V 2912 1558 V 2913 1557 V 2914 1557 V 2915 1556 V 2916 1555 V 2916 1554 V 2917 1553 V 2918 1552 V 2919 1551 V 2920 1550 V 2921 1549 V 2922 1548 V 2923 1548 V 2924 1547 V 2924 1546 V 2925 1545 V 2926 1545 V 2927 1544 V 2928 1543 V 2929 1542 V 2930 1542 V 2931 1541 V 2932 1540 V 2933 1540 V 2934 1539 V 2935 1539 V 2936 1538 V 2937 1538 V 2938 1537 V 2939 1536 V 2940 1536 V 2941 1535 V 2942 1535 V 2943 1534 V 2944 1534 V 2945 1534 V 2946 1533 V 2947 1533 V 2948 1532 V 2949 1532 V 2950 1532 V 2952 1531 V 2953 1531 V 2954 1531 V 2955 1530 V 3049 1460 V 3050 1459 V 3052 1459 V 3053 1459 V 3054 1458 V 3055 1458 V 3056 1458 V 3057 1457 V 3058 1457 V 3059 1456 V 3060 1456 V 3061 1456 V 3062 1455 V 3063 1455 V 3064 1454 V 3065 1454 V 3066 1453 V 3067 1452 V 3068 1452 V 3069 1451 V 3070 1451 V 3071 1450 V 3072 1449 V 3073 1449 V 3074 1448 V 3075 1448 V 3076 1447 V 3077 1446 V 3078 1445 V 3079 1445 V 3080 1444 V 3081 1443 V 3082 1442 V 3082 1441 V 3083 1441 V 3084 1440 V 3085 1439 V 3086 1438 V 3087 1437 V 3088 1436 V 3089 1435 V 3089 1434 V 3090 1433 V 3091 1432 V 3092 1432 V 3093 1430 V 3094 1429 V 3094 1428 V 3095 1427 V 3096 1426 V 3097 1425 V 3098 1424 V 3098 1423 V 3099 1422 V 3100 1421 V 3101 1420 V 3101 1418 V 3102 1417 V 3103 1416 V 3104 1415 V 3104 1413 V 3105 1412 V 3106 1411 V 3106 1410 V 3107 1408 V 3108 1407 V 3108 1406 V 3109 1404 V 3110 1403 V 3110 1401 V 3111 1400 V 3112 1399 V 3112 1397 V 3113 1396 V 3114 1394 V 3114 1393 V 3115 1391 V 3116 1390 V 3116 1388 V 3117 1387 V 3117 1385 V 3118 1383 V 3119 1382 V 3119 1380 V 3120 1379 V 3120 1377 V 2884 1377 V 2884 1379 V 2885 1380 V 2885 1382 V 2886 1383 V 2886 1385 V 2887 1387 V 2887 1388 V 2888 1390 V 2888 1391 V 2889 1393 V 2889 1395 V 2890 1396 V 2890 1398 V 2891 1399 V 2892 1401 V 2892 1402 V 2893 1404 V 2893 1405 V 2894 1407 V 2895 1408 V 2895 1410 V 2896 1411 V 2897 1412 V 2897 1414 V 2898 1415 V 2899 1417 V 2899 1418 V 2900 1419 V 2901 1421 V 2902 1422 V 2902 1423 V 2903 1425 V 2904 1426 V 2905 1427 V 2905 1429 V 2906 1430 V 2907 1431 V 2908 1432 V 2909 1434 V 2910 1435 V 2910 1436 V 2911 1437 V 2912 1439 V 2913 1440 V 2914 1441 V 2915 1442 V 2916 1443 V 2917 1444 V 2918 1445 V 2919 1447 V 2920 1448 V 2921 1449 V 2922 1450 V 2923 1451 V 2924 1452 V 2925 1453 V 2926 1454 V 2927 1455 V 2928 1456 V 2929 1457 V 2930 1458 V 2931 1459 V 2932 1460 V 2933 1461 V 2935 1462 V 2936 1463 V 2937 1464 V 2938 1465 V 2939 1466 V 2940 1467 V 2942 1468 V 2943 1469 V 2944 1469 V 2945 1470 V 2947 1471 V 2948 1472 V 2949 1473 V 2950 1474 V 2952 1474 V 2953 1475 V 2954 1476 V 2956 1477 V 2957 1477 V 2958 1478 V 2960 1479 V 2961 1480 V 2962 1480 V 2964 1481 V 2965 1482 V 2967 1482 V 2968 1483 V 2969 1484 V 2971 1484 V 2972 1485 V 2974 1486 V 2975 1486 V 2977 1487 V 2978 1487 V 2980 1488 V 2981 1489 V 2983 1489 V 2984 1490 V 2986 1490 V 2988 1491 V 2989 1491 V 2991 1492 V 2992 1492 V 2994 1493 V 2996 1493 V 2997 1494 V 2999 1494 V 3000 1495 V 3002 1495 V 3002 1495 V 3004 1495 V 3005 1496 V 3007 1496 V 3009 1497 V 3010 1497 V 3012 1498 V 3014 1498 V 3015 1499 V 3017 1499 V 3018 1500 V 3020 1500 V 3021 1501 V 3023 1501 V 3024 1502 V 3026 1503 V 3027 1503 V 3029 1504 V 3030 1504 V 3032 1505 V 3033 1506 V 3035 1506 V 3036 1507 V 3038 1508 V 3039 1508 V 3040 1509 V 3042 1510 V 3043 1510 V 3045 1511 V 3046 1512 V 3047 1513 V 3049 1513 V 3050 1514 V 3051 1515 V 3053 1516 V 3054 1516 V 3055 1517 V 3056 1518 V 3058 1519 V 3059 1520 V 3060 1521 V 3061 1521 V 3063 1522 V 3064 1523 V 3065 1524 V 3066 1525 V 3067 1526 V 3068 1527 V 3070 1528 V 3071 1529 V 3072 1530 V 3073 1531 V 3074 1532 V 3075 1533 V 3076 1534 V 3077 1535 V 3078 1536 V 3079 1537 V 3080 1538 V 3081 1539 V 3082 1540 V 3083 1541 V 3084 1542 V 3085 1543 V 3086 1544 V 3087 1546 V 3088 1547 V 3089 1548 V 3090 1549 V 3091 1550 V 3092 1551 V 3093 1553 V 3094 1554 V 3095 1555 V 3095 1556 V 3096 1558 V 3097 1559 V 3098 1560 V 3099 1561 V 3100 1563 V 3100 1564 V 3101 1565 V 3102 1567 V 3103 1568 V 3103 1569 V 3104 1571 V 3105 1572 V 3106 1573 V 3106 1575 V 3107 1576 V 3108 1578 V 3108 1579 V 3109 1580 V 3110 1582 V 3110 1583 V 3111 1585 V 3112 1586 V 3112 1588 V 3113 1589 V 3113 1591 V 3114 1592 V 3114 1594 V 3115 1595 V 3115 1597 V 3116 1598 V 3117 1600 V 3117 1602 V 3118 1603 V 3118 1605 V 3118 1606 V 3119 1608 V 3119 1610 V 3120 1611 V 3120 1613 V 2624 1493 a Fb(r)22 b(r)h(r)542 b(r)22 b(r)g(r)404 2438 y Ft(Slik)-5 b(a)30 b(A1.)44 b(Lijev)m(o)32 b(je)h(prik)-5 b(azano)31 b(djelo)m(v)-5 b(anje)33 b(op)s(eratora)e Fm(\033)2622 2453 y Fi(I)2663 2438 y Ft(,)h(a)h(desno)g(in)m(v)m(erznog)g(op)s(e-)841 2556 y(ratora)e Fm(\033)1192 2515 y Fl(\000)p Fr(1)1188 2581 y Fi(I)1287 2556 y Ft(.)p 404 3984 709 4 v 2530 3984 V 404 2921 V 2530 2921 V 1845 3510 a Fa(=)p 404 3629 48 4 v 498 3629 V 593 3629 V 687 3629 V 782 3629 V 876 3629 V 971 3629 V 1065 3629 V 404 3275 V 498 3275 V 593 3275 V 687 3275 V 782 3275 V 876 3275 V 971 3275 V 1065 3275 V 2530 3629 V 2624 3629 V 2719 3629 V 2813 3629 V 2908 3629 V 3002 3629 V 3097 3629 V 3191 3629 V 2530 3275 V 2624 3275 V 2719 3275 V 2813 3275 V 2908 3275 V 3002 3275 V 3097 3275 V 3191 3275 V 522 3984 4 4 v 522 3982 V 522 3980 V 523 3979 V 523 3977 V 523 3975 V 523 3974 V 524 3972 V 524 3971 V 524 3969 V 524 3967 V 525 3966 V 525 3964 V 525 3963 V 525 3961 V 526 3960 V 526 3958 V 526 3956 V 527 3955 V 527 3953 V 527 3952 V 528 3950 V 528 3949 V 528 3947 V 529 3946 V 529 3944 V 529 3943 V 530 3942 V 530 3940 V 530 3939 V 531 3937 V 531 3936 V 531 3934 V 532 3933 V 532 3932 V 532 3930 V 533 3929 V 533 3927 V 533 3926 V 534 3925 V 534 3923 V 535 3922 V 535 3921 V 535 3919 V 536 3918 V 536 3917 V 537 3915 V 537 3914 V 537 3913 V 538 3911 V 538 3910 V 539 3909 V 539 3908 V 539 3906 V 540 3905 V 540 3904 V 541 3903 V 541 3901 V 542 3900 V 542 3899 V 542 3898 V 543 3897 V 543 3895 V 544 3894 V 544 3893 V 545 3892 V 545 3891 V 546 3890 V 546 3889 V 547 3887 V 547 3886 V 548 3885 V 548 3884 V 549 3883 V 549 3882 V 550 3881 V 550 3880 V 551 3879 V 551 3878 V 552 3877 V 552 3875 V 553 3874 V 553 3873 V 554 3872 V 554 3871 V 555 3870 V 555 3869 V 556 3868 V 557 3867 V 557 3866 V 558 3865 V 558 3864 V 559 3864 V 559 3863 V 560 3862 V 560 3861 V 561 3860 V 562 3859 V 562 3858 V 563 3857 V 563 3856 V 564 3855 V 565 3854 V 565 3854 V 566 3853 V 566 3852 V 567 3851 V 568 3850 V 568 3849 V 569 3849 V 570 3848 V 570 3847 V 571 3846 V 571 3845 V 572 3845 V 573 3844 V 573 3843 V 574 3842 V 575 3841 V 575 3841 V 576 3840 V 577 3839 V 577 3839 V 578 3838 V 579 3837 V 579 3836 V 580 3836 V 581 3835 V 581 3834 V 582 3834 V 583 3833 V 584 3832 V 584 3832 V 585 3831 V 586 3831 V 586 3830 V 587 3829 V 588 3829 V 589 3828 V 589 3828 V 590 3827 V 591 3826 V 592 3826 V 592 3825 V 593 3825 V 594 3824 V 595 3824 V 595 3823 V 596 3823 V 597 3822 V 598 3822 V 598 3821 V 599 3821 V 600 3820 V 601 3820 V 602 3819 V 602 3819 V 603 3818 V 604 3818 V 605 3817 V 606 3817 V 606 3817 V 607 3816 V 608 3816 V 609 3815 V 610 3815 V 611 3815 V 611 3814 V 612 3814 V 613 3813 V 614 3813 V 615 3813 V 616 3812 V 616 3812 V 617 3812 V 618 3812 V 619 3811 V 620 3811 V 621 3811 V 622 3810 V 622 3810 V 623 3810 V 624 3810 V 625 3809 V 626 3809 V 627 3809 V 628 3809 V 629 3808 V 630 3808 V 631 3808 V 631 3808 V 632 3808 V 633 3807 V 634 3807 V 635 3807 V 636 3807 V 637 3807 V 638 3807 V 639 3807 V 640 3806 V 640 3806 V 641 3807 V 642 3807 V 642 3807 V 643 3807 V 644 3807 V 645 3807 V 646 3807 V 646 3807 V 647 3807 V 648 3807 V 649 3807 V 650 3807 V 651 3807 V 651 3807 V 652 3807 V 653 3807 V 654 3807 V 654 3807 V 655 3807 V 656 3807 V 657 3807 V 658 3807 V 658 3807 V 659 3807 V 660 3807 V 661 3807 V 661 3806 V 662 3806 V 663 3806 V 664 3806 V 664 3806 V 665 3806 V 666 3806 V 667 3805 V 667 3805 V 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579 3776 V 578 3776 V 578 3775 V 577 3775 V 577 3775 V 576 3774 V 576 3774 V 575 3773 V 575 3773 V 574 3772 V 574 3772 V 573 3772 V 573 3771 V 572 3771 V 572 3770 V 571 3770 V 571 3769 V 570 3769 V 570 3768 V 569 3767 V 569 3767 V 568 3766 V 568 3766 V 567 3765 V 567 3765 V 566 3764 V 566 3763 V 566 3763 V 565 3762 V 565 3762 V 564 3761 V 564 3760 V 563 3760 V 563 3759 V 562 3758 V 562 3758 V 561 3757 V 561 3756 V 560 3756 V 560 3755 V 560 3754 V 559 3753 V 559 3753 V 558 3752 V 558 3751 V 557 3750 V 557 3750 V 556 3749 V 556 3748 V 556 3747 V 555 3746 V 555 3745 V 554 3745 V 554 3744 V 553 3743 V 553 3742 V 553 3741 V 552 3740 V 552 3739 V 551 3739 V 551 3738 V 551 3737 V 550 3736 V 550 3735 V 549 3734 V 549 3733 V 548 3732 V 548 3731 V 548 3730 V 547 3729 V 547 3728 V 546 3727 V 546 3726 V 546 3725 V 545 3724 V 545 3723 V 544 3722 V 544 3721 V 544 3720 V 543 3719 V 543 3718 V 543 3716 V 542 3715 V 542 3714 V 541 3713 V 541 3712 V 541 3711 V 540 3710 V 540 3709 V 540 3707 V 539 3706 V 539 3705 V 538 3704 V 538 3703 V 538 3701 V 537 3700 V 537 3699 V 537 3698 V 536 3696 V 536 3695 V 536 3694 V 535 3693 V 535 3691 V 535 3690 V 534 3689 V 534 3687 V 534 3686 V 533 3685 V 533 3683 V 533 3682 V 532 3681 V 532 3679 V 532 3678 V 531 3677 V 531 3675 V 531 3674 V 530 3672 V 530 3671 V 530 3670 V 529 3668 V 529 3667 V 529 3665 V 528 3664 V 528 3662 V 528 3661 V 527 3659 V 527 3658 V 527 3656 V 526 3655 V 526 3653 V 526 3652 V 526 3650 V 525 3649 V 525 3647 V 525 3646 V 524 3644 V 524 3642 V 524 3641 V 523 3639 V 523 3638 V 523 3636 V 523 3634 V 522 3633 V 522 3631 V 522 3629 V 520 3628 4 355 v 522 3275 4 4 v 522 3273 V 522 3272 V 522 3270 V 523 3268 V 523 3267 V 523 3265 V 523 3263 V 524 3262 V 524 3260 V 524 3259 V 524 3257 V 524 3256 V 525 3254 V 525 3252 V 525 3251 V 525 3249 V 526 3248 V 526 3246 V 526 3245 V 527 3243 V 527 3242 V 527 3240 V 527 3239 V 528 3237 V 528 3236 V 528 3234 V 528 3233 V 529 3231 V 529 3230 V 529 3228 V 530 3227 V 530 3226 V 530 3224 V 530 3223 V 531 3221 V 531 3220 V 531 3219 V 532 3217 V 532 3216 V 532 3215 V 533 3213 V 533 3212 V 533 3211 V 534 3209 V 534 3208 V 534 3207 V 535 3205 V 535 3204 V 535 3203 V 536 3201 V 536 3200 V 536 3199 V 537 3198 V 537 3196 V 537 3195 V 538 3194 V 538 3193 V 538 3191 V 539 3190 V 539 3189 V 540 3188 V 540 3187 V 540 3186 V 541 3184 V 541 3183 V 542 3182 V 542 3181 V 542 3180 V 543 3179 V 543 3177 V 544 3176 V 544 3175 V 544 3174 V 545 3173 V 545 3172 V 546 3171 V 546 3170 V 546 3169 V 547 3168 V 547 3167 V 548 3166 V 548 3165 V 549 3164 V 549 3163 V 549 3162 V 550 3161 V 550 3160 V 551 3159 V 551 3158 V 552 3157 V 552 3156 V 553 3155 V 553 3154 V 554 3153 V 554 3152 V 554 3151 V 555 3150 V 555 3149 V 556 3148 V 556 3147 V 557 3147 V 557 3146 V 558 3145 V 558 3144 V 559 3143 V 559 3142 V 560 3141 V 560 3141 V 561 3140 V 561 3139 V 562 3138 V 562 3137 V 563 3137 V 563 3136 V 564 3135 V 564 3134 V 565 3133 V 565 3133 V 566 3132 V 567 3131 V 567 3131 V 568 3130 V 568 3129 V 569 3128 V 569 3128 V 570 3127 V 570 3126 V 571 3126 V 572 3125 V 572 3124 V 573 3124 V 573 3123 V 574 3122 V 574 3122 V 575 3121 V 576 3121 V 576 3120 V 577 3119 V 577 3119 V 578 3118 V 578 3118 V 579 3117 V 580 3117 V 580 3116 V 581 3115 V 581 3115 V 582 3114 V 583 3114 V 583 3113 V 584 3113 V 585 3112 V 585 3112 V 586 3111 V 586 3111 V 587 3110 V 588 3110 V 588 3110 V 589 3109 V 590 3109 V 590 3108 V 591 3108 V 592 3107 V 592 3107 V 593 3107 V 594 3106 V 594 3106 V 595 3106 V 596 3105 V 596 3105 V 597 3105 V 598 3104 V 598 3104 V 599 3104 V 600 3103 V 600 3103 V 601 3103 V 602 3102 V 602 3102 V 603 3102 V 604 3102 V 605 3101 V 605 3101 V 606 3101 V 607 3101 V 607 3100 V 608 3100 V 609 3100 V 610 3100 V 610 3099 V 611 3099 V 612 3099 V 612 3099 V 613 3099 V 614 3099 V 615 3098 V 615 3098 V 616 3098 V 617 3098 V 618 3098 V 618 3098 V 619 3098 V 620 3098 V 621 3098 V 621 3097 V 622 3097 V 623 3097 V 624 3097 V 625 3097 V 625 3097 V 626 3097 V 627 3097 V 628 3097 V 629 3097 V 629 3097 V 630 3097 V 631 3097 V 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3703 V 3107 3702 V 3107 3700 V 3107 3699 V 3108 3698 V 3108 3696 V 3108 3695 V 3109 3694 V 3109 3692 V 3109 3691 V 3110 3690 V 3110 3688 V 3110 3687 V 3111 3686 V 3111 3684 V 3111 3683 V 3112 3681 V 3112 3680 V 3112 3679 V 3112 3677 V 3113 3676 V 3113 3674 V 3113 3673 V 3114 3671 V 3114 3670 V 3114 3668 V 3114 3667 V 3115 3666 V 3115 3664 V 3115 3663 V 3116 3661 V 3116 3660 V 3116 3658 V 3116 3656 V 3117 3655 V 3117 3653 V 3117 3652 V 3117 3650 V 3118 3649 V 3118 3647 V 3118 3646 V 3118 3644 V 3118 3642 V 3119 3641 V 3119 3639 V 3119 3638 V 3119 3636 V 3120 3634 V 3120 3633 V 3120 3631 V 3120 3629 V 3119 3628 4 355 v 3120 3275 4 4 v 3120 3273 V 3120 3272 V 3119 3270 V 3119 3268 V 3119 3267 V 3119 3265 V 3118 3263 V 3118 3262 V 3118 3260 V 3117 3259 V 3117 3257 V 3117 3256 V 3116 3254 V 3116 3252 V 3116 3251 V 3116 3249 V 3115 3248 V 3115 3246 V 3115 3245 V 3114 3243 V 3114 3242 V 3114 3240 V 3113 3239 V 3113 3238 V 3113 3236 V 3112 3235 V 3112 3233 V 3112 3232 V 3111 3230 V 3111 3229 V 3111 3228 V 3110 3226 V 3110 3225 V 3110 3223 V 3110 3222 V 3109 3221 V 3109 3219 V 3108 3218 V 3108 3217 V 3108 3215 V 3107 3214 V 3107 3213 V 3107 3212 V 3106 3210 V 3106 3209 V 3106 3208 V 3105 3207 V 3105 3205 V 3105 3204 V 3104 3203 V 3104 3202 V 3104 3200 V 3103 3199 V 3103 3198 V 3102 3197 V 3102 3196 V 3102 3195 V 3101 3193 V 3101 3192 V 3101 3191 V 3100 3190 V 3100 3189 V 3099 3188 V 3099 3187 V 3099 3186 V 3098 3184 V 3098 3183 V 3098 3182 V 3097 3181 V 3097 3180 V 3096 3179 V 3096 3178 V 3096 3177 V 3095 3176 V 3095 3175 V 3094 3174 V 3094 3173 V 3094 3172 V 3093 3171 V 3093 3170 V 3092 3169 V 3092 3168 V 3092 3168 V 3091 3167 V 3091 3166 V 3090 3165 V 3090 3164 V 3089 3163 V 3089 3162 V 3089 3161 V 3088 3160 V 3088 3160 V 3087 3159 V 3087 3158 V 3086 3157 V 3086 3156 V 3086 3156 V 3085 3155 V 3085 3154 V 3084 3153 V 3084 3152 V 3083 3152 V 3083 3151 V 3082 3150 V 3082 3149 V 3082 3149 V 3081 3148 V 3081 3147 V 3080 3147 V 3080 3146 V 3079 3145 V 3079 3145 V 3078 3144 V 3078 3143 V 3077 3143 V 3077 3142 V 3077 3141 V 3076 3141 V 3076 3140 V 3075 3140 V 3075 3139 V 3074 3138 V 3074 3138 V 3073 3137 V 3073 3137 V 3072 3136 V 3072 3136 V 3071 3135 V 3071 3135 V 3070 3134 V 3070 3134 V 3069 3133 V 3069 3133 V 3068 3132 V 3068 3132 V 3067 3131 V 3067 3131 V 3066 3130 V 3066 3130 V 3065 3130 V 3065 3129 V 3064 3129 V 3064 3128 V 3063 3128 V 3063 3128 V 3062 3127 V 3062 3127 V 3061 3127 V 3061 3126 V 3060 3126 V 3060 3126 V 3059 3125 V 3059 3125 V 3058 3125 V 3058 3124 V 3057 3124 V 3056 3124 V 3056 3124 V 3055 3123 V 3055 3123 V 3054 3123 V 3054 3123 V 3053 3123 V 3053 3122 V 3052 3122 V 3052 3122 V 3051 3122 V 3051 3122 V 3050 3122 V 3049 3121 V 2955 3074 V 2954 3074 V 2954 3074 V 2953 3074 V 2953 3075 V 2953 3075 V 2952 3075 V 2952 3075 V 2951 3075 V 2951 3075 V 2950 3075 V 2950 3075 V 2949 3075 V 2949 3075 V 2948 3075 V 2948 3075 V 2947 3075 V 2947 3075 V 2947 3075 V 2946 3075 V 2946 3075 V 2945 3075 V 2945 3075 V 2944 3075 V 2944 3074 V 2943 3074 V 2943 3074 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2910 3033 V 2910 3032 V 2909 3031 V 2909 3030 V 2909 3030 V 2908 3029 V 2908 3028 V 2907 3027 V 2907 3026 V 2907 3025 V 2906 3024 V 2906 3023 V 2906 3022 V 2905 3021 V 2905 3020 V 2905 3019 V 2905 3018 V 2904 3017 V 2904 3016 V 2904 3015 V 2903 3014 V 2903 3013 V 2903 3012 V 2902 3011 V 2902 3010 V 2902 3009 V 2901 3008 V 2901 3006 V 2901 3005 V 2900 3004 V 2900 3003 V 2900 3002 V 2899 3001 V 2899 3000 V 2899 2999 V 2899 2997 V 2898 2996 V 2898 2995 V 2898 2994 V 2897 2993 V 2897 2991 V 2897 2990 V 2896 2989 V 2896 2988 V 2896 2986 V 2896 2985 V 2895 2984 V 2895 2983 V 2895 2981 V 2894 2980 V 2894 2979 V 2894 2977 V 2894 2976 V 2893 2975 V 2893 2973 V 2893 2972 V 2892 2971 V 2892 2969 V 2892 2968 V 2892 2966 V 2891 2965 V 2891 2964 V 2891 2962 V 2891 2961 V 2890 2959 V 2890 2958 V 2890 2956 V 2890 2955 V 2889 2954 V 2889 2952 V 2889 2951 V 2888 2949 V 2888 2948 V 2888 2946 V 2888 2945 V 2887 2943 V 2887 2941 V 2887 2940 V 2887 2938 V 2886 2937 V 2886 2935 V 2886 2934 V 2886 2932 V 2885 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V 2686 3401 V 2686 3400 V 2686 3400 V 2685 3399 V 2685 3398 V 2684 3398 V 2684 3397 V 2683 3396 V 2683 3395 V 2682 3394 V 2682 3394 V 2682 3393 V 2681 3392 V 2681 3391 V 2680 3390 V 2680 3389 V 2679 3389 V 2679 3388 V 2679 3387 V 2678 3386 V 2678 3385 V 2677 3384 V 2677 3383 V 2676 3382 V 2676 3381 V 2676 3381 V 2675 3380 V 2675 3379 V 2674 3378 V 2674 3377 V 2674 3376 V 2673 3375 V 2673 3374 V 2672 3373 V 2672 3372 V 2672 3371 V 2671 3370 V 2671 3369 V 2670 3368 V 2670 3366 V 2670 3365 V 2669 3364 V 2669 3363 V 2669 3362 V 2668 3361 V 2668 3360 V 2667 3359 V 2667 3358 V 2667 3357 V 2666 3355 V 2666 3354 V 2666 3353 V 2665 3352 V 2665 3351 V 2664 3350 V 2664 3348 V 2664 3347 V 2663 3346 V 2663 3345 V 2663 3343 V 2662 3342 V 2662 3341 V 2662 3340 V 2661 3338 V 2661 3337 V 2661 3336 V 2660 3334 V 2660 3333 V 2660 3332 V 2659 3331 V 2659 3329 V 2659 3328 V 2658 3326 V 2658 3325 V 2658 3324 V 2657 3322 V 2657 3321 V 2657 3320 V 2656 3318 V 2656 3317 V 2656 3315 V 2655 3314 V 2655 3312 V 2655 3311 V 2654 3309 V 2654 3308 V 2654 3307 V 2653 3305 V 2653 3304 V 2653 3302 V 2652 3301 V 2652 3299 V 2652 3297 V 2652 3296 V 2651 3294 V 2651 3293 V 2651 3291 V 2650 3290 V 2650 3288 V 2650 3286 V 2649 3285 V 2649 3283 V 2649 3282 V 2649 3280 V 2648 3278 V 2648 3277 V 2648 3275 V 2646 3273 4 355 v 404 4218 a Ft(Slik)-5 b(a)30 b(A2.)44 b(Slik)m(o)m(viti)30 b(prik)-5 b(az)32 b(relacije)f(\(A.1\).)p 404 5173 945 4 v 2530 5173 V 404 4464 V 2530 4464 V 1845 4817 a Fa(=)p 404 4819 48 4 v 498 4819 V 593 4819 V 687 4819 V 782 4819 V 876 4819 V 971 4819 V 1065 4819 V 1160 4819 V 1254 4819 V 2530 4819 V 2624 4819 V 2719 4819 V 2813 4819 V 2908 4819 V 3002 4819 V 3097 4819 V 3191 4819 V 3286 4819 V 3380 4819 V 522 5173 4 4 v 522 5171 V 522 5169 V 523 5168 V 523 5166 V 523 5164 V 523 5163 V 524 5161 V 524 5160 V 524 5158 V 524 5156 V 525 5155 V 525 5154 V 525 5152 V 525 5151 V 526 5149 V 526 5147 V 526 5146 V 527 5144 V 527 5143 V 527 5141 V 528 5140 V 528 5138 V 528 5137 V 529 5135 V 529 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3138 4897 V 3138 4896 V 3137 4894 V 3137 4893 V 3137 4892 V 3136 4891 V 3136 4890 V 3135 4888 V 3135 4887 V 3135 4886 V 3134 4885 V 3134 4883 V 3134 4882 V 3133 4881 V 3133 4880 V 3133 4878 V 3132 4877 V 3132 4876 V 3132 4874 V 3131 4873 V 3131 4872 V 3131 4870 V 3130 4869 V 3130 4867 V 3130 4866 V 3129 4865 V 3129 4863 V 3129 4862 V 3128 4860 V 3128 4859 V 3128 4858 V 3127 4856 V 3127 4855 V 3127 4853 V 3126 4852 V 3126 4850 V 3126 4849 V 3125 4847 V 3125 4846 V 3125 4844 V 3125 4843 V 3124 4841 V 3124 4840 V 3124 4838 V 3123 4836 V 3123 4835 V 3123 4833 V 3123 4832 V 3122 4830 V 3122 4829 V 3122 4827 V 3121 4825 V 3121 4824 V 3121 4822 V 3121 4820 V 3120 4819 V 404 5408 a Ft(Slik)-5 b(a)30 b(A3.)44 b(Slik)m(o)m(viti)30 b(prik)-5 b(az)32 b(relacije)f(\(A.2\).)p eop %%Page: 48 51 48 50 bop 257 -89 a Fs(DOD)m(A)-8 b(T)g(AK)32 b(A.)66 b(GR)m(UP)-8 b(A)32 b(PLETENICA)1787 b Ft(48)404 294 y(Iz)44 b(slik)m(e)f(je)g(tak)m(o)s(d)p 1076 241 31 4 v(er)h(jasno)g(da)f(op)m(\023)-46 b(cenito,)46 b Fm(\033)2132 309 y Fi(I)2215 294 y Ft(na)e(neku)g(p)s(otenciju)f(ne)h(da)5 b(je)44 b(iden)m(titet.)257 474 y(Samo)33 b(u)g(sp)s(ecijalnom)f(slu)m (\024)-46 b(ca)5 b(ju)33 b(k)-5 b(ada)33 b(je)h Fm(\033)1875 438 y Fr(2)1871 499 y Fi(I)1943 474 y Ft(=)29 b(1,)k(za)h(sv)-5 b(aki)33 b Fm(I)8 b Ft(,)33 b(grupa)h(pletenica)e(sv)m(o)s(di)i(se)g (na)257 655 y(grupu)f(prem)m(utacija.)p 1349 1865 473 4 v 2530 1865 V 1349 1157 V 2530 1157 V 1443 1970 a(1)1443 1120 y(1)2624 1970 y(1)2624 1120 y(1)1679 1970 y(2)1679 1120 y(2)2860 1970 y(2)2860 1120 y(2)p 2646 1864 4 709 v 2882 1864 V 1467 1865 4 4 v 1467 1864 V 1467 1862 V 1468 1860 V 1468 1859 V 1468 1857 V 1468 1855 V 1469 1854 V 1469 1852 V 1469 1851 V 1470 1849 V 1470 1848 V 1470 1846 V 1470 1844 V 1471 1843 V 1471 1841 V 1471 1840 V 1472 1838 V 1472 1837 V 1472 1835 V 1473 1834 V 1473 1832 V 1473 1831 V 1474 1829 V 1474 1828 V 1474 1826 V 1474 1825 V 1475 1824 V 1475 1822 V 1475 1821 V 1476 1819 V 1476 1818 V 1476 1817 V 1477 1815 V 1477 1814 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1361 V 1528 1361 V 1529 1361 V 1529 1361 V 1530 1360 V 1530 1360 V 1531 1360 V 1532 1360 V 1532 1359 V 1533 1359 V 1533 1359 V 1534 1359 V 1534 1358 V 1535 1358 V 1535 1358 V 1536 1358 V 1536 1358 V 1537 1358 V 1538 1357 V 1632 1310 V 1633 1310 V 1633 1310 V 1633 1311 V 1634 1311 V 1634 1311 V 1635 1311 V 1635 1311 V 1636 1311 V 1636 1311 V 1637 1311 V 1637 1311 V 1638 1311 V 1638 1311 V 1639 1311 V 1639 1311 V 1639 1311 V 1640 1311 V 1640 1311 V 1641 1311 V 1641 1311 V 1642 1311 V 1642 1311 V 1643 1311 V 1643 1310 V 1644 1310 V 1644 1310 V 1644 1310 V 1645 1310 V 1645 1310 V 1646 1310 V 1646 1310 V 1647 1309 V 1647 1309 V 1647 1309 V 1648 1309 V 1648 1309 V 1649 1308 V 1649 1308 V 1650 1308 V 1650 1308 V 1651 1308 V 1651 1307 V 1651 1307 V 1652 1307 V 1652 1306 V 1653 1306 V 1653 1306 V 1653 1306 V 1654 1305 V 1654 1305 V 1655 1305 V 1655 1304 V 1656 1304 V 1656 1304 V 1656 1303 V 1657 1303 V 1657 1302 V 1658 1302 V 1658 1302 V 1658 1301 V 1659 1301 V 1659 1300 V 1660 1300 V 1660 1299 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1351 V 1631 1352 V 1632 1352 V 1632 1353 V 1633 1353 V 1634 1354 V 1635 1354 V 1635 1355 V 1636 1355 V 1637 1356 V 1638 1357 V 1638 1357 V 1639 1358 V 1640 1359 V 1640 1359 V 1641 1360 V 1642 1360 V 1642 1361 V 1643 1362 V 1644 1362 V 1645 1363 V 1645 1364 V 1646 1365 V 1647 1365 V 1647 1366 V 1648 1367 V 1649 1367 V 1649 1368 V 1650 1369 V 1651 1370 V 1651 1370 V 1652 1371 V 1653 1372 V 1653 1373 V 1654 1373 V 1655 1374 V 1655 1375 V 1656 1376 V 1656 1377 V 1657 1378 V 1658 1378 V 1658 1379 V 1659 1380 V 1659 1381 V 1660 1382 V 1661 1383 V 1661 1384 V 1662 1384 V 1662 1385 V 1663 1386 V 1664 1387 V 1664 1388 V 1665 1389 V 1665 1390 V 1666 1391 V 1666 1392 V 1667 1393 V 1668 1394 V 1668 1395 V 1669 1396 V 1669 1397 V 1670 1398 V 1670 1399 V 1671 1400 V 1671 1401 V 1672 1402 V 1672 1403 V 1673 1404 V 1674 1405 V 1674 1406 V 1675 1407 V 1675 1408 V 1676 1409 V 1676 1410 V 1677 1411 V 1677 1413 V 1678 1414 V 1678 1415 V 1678 1416 V 1679 1417 V 1679 1418 V 1680 1419 V 1680 1420 V 1681 1422 V 1681 1423 V 1682 1424 V 1682 1425 V 1683 1426 V 1683 1428 V 1684 1429 V 1684 1430 V 1684 1431 V 1685 1433 V 1685 1434 V 1686 1435 V 1686 1436 V 1687 1438 V 1687 1439 V 1687 1440 V 1688 1441 V 1688 1443 V 1689 1444 V 1689 1445 V 1689 1447 V 1690 1448 V 1690 1449 V 1691 1451 V 1691 1452 V 1691 1453 V 1692 1455 V 1692 1456 V 1692 1458 V 1693 1459 V 1693 1460 V 1693 1462 V 1694 1463 V 1694 1465 V 1695 1466 V 1695 1467 V 1695 1469 V 1696 1470 V 1696 1472 V 1696 1473 V 1696 1475 V 1697 1476 V 1697 1478 V 1697 1479 V 1698 1481 V 1698 1482 V 1698 1484 V 1699 1485 V 1699 1487 V 1699 1488 V 1700 1490 V 1700 1492 V 1700 1493 V 1700 1495 V 1701 1496 V 1701 1498 V 1701 1500 V 1701 1501 V 1702 1503 V 1702 1504 V 1702 1506 V 1702 1508 V 1703 1509 V 1703 1511 V 404 2100 a(Slik)-5 b(a)30 b(A4.)44 b(Bogatstv)m(o)33 b(grup)s(e)f(pletenica)g(u)h(usp)s(oredbi)g(s)g(grup) s(om)e(p)s(erm)m(utacija.)404 2517 y(Iz)42 b(relacija)d(\(A.1\))i(i)g (\(A.2\))g(lak)m(o)g(mo)m(\024)-46 b(zemo)40 b(o)s(drediti)g(jedno)s (dimenzijsk)m(e)h(reprezen)m(tacije)257 2697 y(grup)s(e)33 b(pletenica.)43 b(Jedno)s(dimenzijsk)-5 b(a)31 b(reprezen)m(tacija)j (je)e(k)m(om)m(utativna)g(pa)h(vrijedi:)1355 2958 y Fm(\037)p Ft(\()p Fm(\033)1509 2973 y Fr(1)1549 2958 y Ft(\))27 b(=)h Fm(\037)p Ft(\()p Fm(\033)1872 2973 y Fr(2)1912 2958 y Ft(\))f(=)h Fm(:)17 b(:)g(:)27 b Ft(=)g Fm(\037)p Ft(\()p Fm(\033)2480 2973 y Fi(N)7 b Fl(\000)p Fr(1)2638 2958 y Ft(\))p Fm(:)873 b Ft(\(A.3\))257 3219 y(Razli)m(\024)-46 b(cite)31 b(reprezen)m(tacije)j(parametriziramo)29 b(parametrom)h Fm(\022)s Ft(,)1123 3480 y Fm(\037)1184 3495 y Fi(\022)1223 3480 y Ft(\()p Fm(\033)1316 3495 y Fi(J)1365 3480 y Ft(\))e(=)f(exp)q (\()p Fm(i\022)s Ft(\))p Fm(;)45 b Ft(za)28 b(sv)-5 b(aki)28 b(1)f Fp(\024)h Fm(J)37 b Fp(\024)28 b Fm(N)33 b Fp(\000)22 b Ft(1)p Fm(;)641 b Ft(\(A.4\))257 3741 y(gdje)22 b(je)g(0)28 b Fp(\024)g Fm(\022)j(<)c Ft(2)p Fm(\031)t Ft(,)d(ali)c(ina)m(\024)-46 b(ce)21 b(proizv)m(oljan,)d(\024)-44 b(sto)22 b(o)s(dgo)m(v)-5 b(ara)18 b(\024)-46 b(cinjenici)20 b(da)i(p)s(osto)5 b(ji)21 b(b)s(esk)m(ona)m(\024)-46 b(cno)257 3921 y(mnogo)40 b(jedno)s(dimenzijskih)f(reprezen)m(tacija)i(grup)s(e)g(pletenica,)h (ozna)m(\024)-46 b(cenih)41 b(k)m(on)m(tin)m(uiranim)257 4102 y(statisti)m(\024)-46 b(ckim)31 b(parametrom)g Fm(\022)s Ft(.)404 4283 y(U)k(slu)m(\024)-46 b(ca)5 b(ju)35 b(k)-5 b(ada)35 b(se)h(opisuju)f(k)m(ompliciraniji)30 b(\014zik)-5 b(alni)33 b(susta)m(vi,)k(gdje)e(su)h(v)-5 b(alne)34 b(funk)m(cije)257 4463 y(m)m(ultipleti,)48 b(p)s(otrebno)f(je)g (razmotriti)e(vi)-5 b(\024)-44 b(sedimenzijsk)m(e)47 b(reprezen)m(tacije)i(grup)s(e)e(pletenica.)257 4644 y(T)-8 b(ak)m(o)s(d)p 487 4591 31 4 v(er)37 b(je)e(u)h(o)s(dred)p 1044 4591 V(enim)e(\014zik)-5 b(alnim)33 b(situacijama)f(p)s(otrebno)k (razmatrati)d(anione)i(na)g(plo-)257 4824 y(hama)43 b(s)i (netrivijalnim)40 b(gen)m(usom,)47 b(ili)41 b(zakrivljenim)h(plohama.) 75 b(No)44 b(o)m(v)-5 b(a)5 b(j)44 b(kratki)g(pregled)257 5005 y(nekih)35 b(sv)m(o)5 b(jsta)m(v)-5 b(a)35 b(grup)s(e)f(pletenica) f(je)h(trebao)g(uk)-5 b(azati)33 b(na)h(p)s(orijeklo)e(in)m (termedijarne)h(stati-)257 5185 y(stik)m(e)e(u)f(dvije)g(dimenzije,)f (te)h(zain)m(teresirane)g(za)g(sv)m(e)i(neizre)m(\024)-46 b(ceno,)32 b(upu)m(\023)-46 b(cujemo)30 b(na)g(p)s(osto)5 b(je)m(\023)-46 b(cu)257 5366 y(literaturu)31 b([40].)p eop %%Page: 49 52 49 51 bop 257 1082 a Fv(Do)6 b(datak)79 b(B)257 1622 y(Matemati)-6 b(\024)-110 b(cki)78 b(iden)-6 b(titeti)257 2228 y Fk(B1)257 2507 y Ft(Dok)h(a)m(\024)-46 b(zimo)31 b(relaciju)g(\(2.5\),)h(k)m(o)5 b(ju)33 b(smo)f(k)m(oristili)e(u)j (drugom)f(p)s(ogla)m(vlju)1306 2677 y Fi(N)1278 2702 y Fj(X)1281 2884 y Fi(i)p Fr(=1)1414 2614 y Fj(0)1414 2763 y(@)1515 2677 y Fi(N)1487 2702 y Fj(X)1491 2886 y Fi(j)t Fl(6)p Fr(=)p Fi(i)1758 2718 y Ft(1)p 1633 2762 298 4 v 1633 2853 a Fm(x)1688 2868 y Fi(i)1739 2853 y Fp(\000)23 b Fm(x)1894 2868 y Fi(j)1941 2614 y Fj(1)1941 2763 y(A)2013 2637 y Fr(2)2081 2785 y Ft(=)2212 2677 y Fi(N)2184 2702 y Fj(X)2188 2886 y Fi(j)t Fl(6)p Fr(=)p Fi(i)2512 2718 y Ft(1)p 2331 2762 413 4 v 2331 2853 a(\()p Fm(x)2424 2868 y Fi(i)2474 2853 y Fp(\000)g Fm(x)2629 2868 y Fi(j)2666 2853 y Ft(\))2704 2824 y Fr(2)2753 2785 y Fm(:)257 3040 y Ft(Raspi)-5 b(\024)-44 b(simo)31 b(lijevu)g(stran)m (u)j(gornjeg)e(izraza)749 3204 y Fi(N)721 3229 y Fj(X)724 3412 y Fi(i)p Fr(=1)857 3141 y Fj(0)857 3291 y(@)958 3204 y Fi(N)930 3229 y Fj(X)934 3414 y Fi(j)t Fl(6)p Fr(=)p Fi(i)1201 3245 y Ft(1)p 1077 3289 298 4 v 1077 3381 a Fm(x)1132 3396 y Fi(i)1182 3381 y Fp(\000)23 b Fm(x)1337 3396 y Fi(j)1384 3141 y Fj(1)1384 3291 y(A)1456 3164 y Fr(2)1524 3312 y Ft(=)1656 3204 y Fi(N)1627 3229 y Fj(X)1631 3414 y Fi(j)t Fl(6)p Fr(=)p Fi(i)1956 3245 y Ft(1)p 1774 3289 413 4 v 1774 3381 a(\()p Fm(x)1867 3396 y Fi(i)1917 3381 y Fp(\000)g Fm(x)2072 3396 y Fi(j)2109 3381 y Ft(\))2147 3352 y Fr(2)2218 3312 y Ft(+)2387 3204 y Fi(N)2359 3229 y Fj(X)2316 3414 y Fi(j)t Fl(6)p Fr(=)p Fi(i)p Fl(6)p Fr(=)p Fi(k)2899 3245 y Ft(1)p 2548 3289 753 4 v 2548 3381 a(\()p Fm(x)2641 3396 y Fi(i)2691 3381 y Fp(\000)g Fm(x)2846 3396 y Fi(j)2883 3381 y Ft(\)\()p Fm(x)3014 3396 y Fi(i)3064 3381 y Fp(\000)g Fm(x)3219 3396 y Fi(k)3262 3381 y Ft(\))3310 3312 y Fm(:)243 b Ft(\(B.1\))257 3568 y(Vidimo)30 b(da)j(sada)g(moramo)d(dok)-5 b(azati)32 b(sljede)m(\023)-46 b(ci)32 b(iden)m(titet)1499 3703 y Fi(N)1471 3728 y Fj(X)1429 3912 y Fi(j)t Fl(6)p Fr(=)p Fi(i)p Fl(6)p Fr(=)p Fi(k)2012 3743 y Ft(1)p 1660 3787 V 1660 3879 a(\()p Fm(x)1753 3894 y Fi(i)1804 3879 y Fp(\000)22 b Fm(x)1958 3894 y Fi(j)1995 3879 y Ft(\)\()p Fm(x)2126 3894 y Fi(i)2177 3879 y Fp(\000)g Fm(x)2331 3894 y Fi(k)2374 3879 y Ft(\))2450 3811 y(=)28 b(0)p Fm(:)950 b Ft(\(B.2\))257 4070 y(U)41 b(gornjem)g(izrazu)f(\(B.2\))h (su)h(svi)f(indeksi)g("njemi")e(\(sumiramo)g(p)s(o)i(njima\),)g(pa)g (mo)m(\024)-46 b(zemo)257 4250 y(napra)m(vititi)31 b(supstitucije)h Fm(i)c Fp($)g Fm(j)38 b Ft(ili)30 b Fm(i)e Fp($)f Fm(k)s Ft(,)33 b(pa)f(o)m(\024)-46 b(cito)32 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b(=)f Fp(\000)p Ft(Im)p Fm(f)11 b Ft(\()p Fm(x)24 b Fp(\000)h Fm(i")p Ft(\),)37 b(i)e(Re)p Fm(f)11 b Ft(\()p Fm(x)24 b Ft(+)h Fm(i")p Ft(\))33 b(=)g(Re)p Fm(f)11 b Ft(\()p Fm(x)25 b Fp(\000)g Fm(i")p Ft(\).)53 b(Iz)36 b(\(B.12\))g(onda)257 4831 y(slijedi)599 4981 y Fj(Z)699 5099 y Fm(dx)822 5002 y Fj(h)861 5099 y Ft(6)p Fm(i)17 b Ft(\(Re)p Fm(f)11 b Ft(\()p Fm(x)22 b Ft(+)g Fm(i")p Ft(\)\))1540 5050 y Fr(2)1596 5099 y Ft(Im)o Fm(f)11 b Ft(\()p Fm(x)23 b Ft(+)f Fm(i")p Ft(\))g Fp(\000)g Ft(2)p Fm(i)17 b Ft(\(Im)o Fm(f)11 b Ft(\()p Fm(x)22 b Ft(+)g Fm(i")p Ft(\)\))2903 5050 y Fr(3)2943 5002 y Fj(i)3010 5099 y Ft(=)27 b(0)p Fm(:)342 b Ft(\(B.15\))257 5366 y(Uvr)-5 b(\024)-44 b(sta)m(v)-5 b(anjem)33 b(relacija)e(\(B.13\))h(u)h(gornji)e(izraz)h(lak)m(o)g (dobiv)-5 b(amo)31 b(tra)m(\024)-46 b(zeni)32 b(iden)m(titet)g (\(B.9\).)p eop %%Page: 52 55 52 54 bop 257 1082 a Fv(Literatura)306 1595 y Ft([1])49 b(N.)33 b(Ark)-5 b(ani-Hamed,)31 b(S.)i(Dimop)s(oulos)c(i)j(G.)g(Dv)-5 b(ali,)62 b Fs(Ph)m(ys.)35 b(Rev.)e Fu(D59)g Ft(\(1999\))e(086044.)306 1858 y([2])49 b(N.)35 b(Seib)s(erg)g(i)f(E.)i(Witten,)71 b Fs(Nucl.)35 b(Ph)m(ys.)i Fu(B426)e Ft(\(1994\))f(19;)i(\(E\))71 b Fs(Nucl.)35 b(Ph)m(ys.)i Fu(B430)458 2039 y Ft(\(1994\))31 b(485.)306 2302 y([3])49 b(J.)33 b(M.)g(Leinaas)f(i)f(J.)i(Myrheim,)f Fs(Nuo)m(v)m(o)i(Cim.)d Fu(B37)p Ft(,)i(\(1977\))e(1.)306 2565 y([4])49 b(F.)32 b(D.)g(M.)h(Haldane,)65 b Fs(Ph)m(ys.)34 b(Rev.)g(Lett.)e Fu(67)h Ft(\(1991\))e(937.)306 2828 y([5])49 b(A.)33 b(Jevic)m(ki)f(i)g(B.)h(Sakita,)64 b Fs(Nucl.)33 b(Ph)m(ys.)h Fu(B165)e Ft(\(1980\))g(511.)306 3091 y([6])49 b(L.)34 b(Jonk)m(e,)i("Solitoni)31 b(u)j (Calogero-Sutherlando)m(v)m(om)f(mo)s(delu",)g(magistarski)f(rad,)j (Za-)458 3271 y(greb,)e(1997.)306 3534 y([7])49 b(I.)33 b(Andri)m(\023)-46 b(c,)32 b(V.)h(Bardek)g(i)f(L.)g(Jonk)m(e,)67 b Fs(Fizik)-5 b(a)30 b Fu(B4)70 b Ft(\(1995\))31 b(93.)306 3797 y([8])49 b(G.)41 b(Dunne,)k Fq(Self-Dual)d(Chern-Simons)g(The)-5 b(ories)p Ft(,)43 b(Lecture)g(notes)f(in)g(Ph)m(ysics-)h(New)458 3978 y(Series)33 b(m:)43 b(Monographs)33 b(36,)f(Springer,)g(1995.)306 4241 y([9])49 b(R.)27 b(Jac)m(kiw)g(i)f(S.)h(Y.)g(Pi,)55 b Fs(Ph)m(ys.)29 b(Rev.)e(Lett.)g Fu(64)g Ft(\(1990\))f(2969)f(;)58 b Fs(Ph)m(ys.)29 b(Rev.)e Fu(D42)g Ft(\(1990\))458 4421 y(3500)32 b(;)g Fs(Prog.)h(Theor.)g(Ph)m(ys.)h(Suppl)p Ft(.)f(107,)f(\(1992\))f(1.)257 4684 y([10])49 b(I.)33 b(Andri)m(\023)-46 b(c)32 b(i)g(V.)g(Bardek,)66 b Fs(Ph)m(ys.)35 b(Rev.)e Fu(D47)g Ft(\(1993\))e(5546.)257 4947 y([11])49 b(I.)33 b(Andri)m(\023)-46 b(c,)32 b(V.)h(Bardek)g(i)f(L.)g(Jonk)m(e,) 67 b Fs(Ph)m(ys.)34 b(Rev.)f Fu(D59)g Ft(\(1999\))e(107702.)257 5210 y([12])49 b(F.)33 b(Calogero,)66 b Fs(J.)34 b(Math.)f(Ph)m(ys.)j Fu(10)d Ft(\(1969\))f(2191,)h(2197;)67 b Fs(J.)33 b(Math.)h(Ph)m(ys.)h Fu(12)f Ft(\(1971\))458 5391 y(419.)1980 5674 y(52)p eop %%Page: 53 56 53 55 bop 257 -89 a Fs(LITERA)-8 b(TURA)2789 b Ft(53)257 294 y([13])49 b(B.)25 b(Sutherland,)54 b Fs(Ph)m(ys.)28 b(Rev.)e Fu(A4)f Ft(\(1971\))f(2019;)55 b Fs(Ph)m(ys.)27 b(Rev.)g Fu(A5)e Ft(\(1972\))f(1372;)55 b Fs(Ph)m(ys.)458 474 y(Rev.)33 b(Lett.)g Fu(34)g Ft(\(1975\))e(1083.)257 738 y([14])49 b(Z.)32 b(N.)h(C.)g(Ha,)65 b Fs(Nucl.)32 b(Ph)m(ys.)j Fu(B435)d Ft(\(1995\))g(604.)257 1002 y([15])49 b(Andri)m(\023)-46 b(c)32 b(i)g(V.)h(Bardek,)66 b Fs(J.)32 b(Ph)m(ys.)j Fu(A21)d Ft(\(1988\))g(2847;)64 b Fs(J.)32 b(Ph)m(ys.)j Fu(A24)d Ft(\(1991\))g(353.)257 1265 y([16])49 b(J.)33 b(A.)f(Minahan)g(i)g(A.)h(P)-8 b(.)33 b(P)m(olyc)m(hronak)m (os,)66 b Fs(Ph)m(ys.)35 b(Lett.)e Fu(B312)f Ft(\(1993\))f(155.)257 1529 y([17])49 b(A.)39 b(Jevic)m(ki,)82 b Fs(Nucl.)39 b(Ph)m(ys.)i Fu(B376)e Ft(\(1992\))f(75;)k(J.)d(P)m(olc)m(hinski,)i ("What)e(is)f(string)h(the-)458 1709 y(ory?",)33 b(NSF-ITP-94-97,)e (hep-th/9411028.)257 1973 y([18])49 b(F.)32 b(D.)g(M.)h(Haldane,)64 b Fs(Ph)m(ys.)34 b(Rev.)f(Lett.)g Fu(60)f Ft(\(1988\))f(635;)h(B.)h(S.) f(Shastry)-8 b(,)66 b Fs(Ph)m(ys.)34 b(Rev.)458 2153 y(Lett.)f Fu(60)f Ft(\(1988\))g(639.)257 2417 y([19])49 b(I.)33 b(Andri)m(\023)-46 b(c,)32 b(V.)h(Bardek)g(i)f(L.)g(Jonk)m(e,) 67 b Fs(J.)33 b(Ph)m(ys.)h Fu(A30)e Ft(\(1997\))g(717.)257 2681 y([20])49 b(Andri)m(\023)-46 b(c,)32 b(A.)h(Jevic)m(ki)g(i)f(H.)g (Levine,)66 b Fs(Nucl.)32 b(Ph)m(ys.)j Fu(B215)d Ft(\(1983\))f(307.)257 2944 y([21])49 b(S.-)26 b(J.)g(Kim,)54 b Fs(Ph)m(ys.)28 b(Lett.)e Fu(B343)g Ft(\(1995\))f(244)h(;)i(S.-)e(J.)h(Kim)d(i)h(C.)i (Lee,)56 b Fs(Ph)m(ys.)28 b(Rev.)f Fu(D55)458 3125 y Ft(\(1997\))k(2227.)257 3388 y([22])49 b(I.)36 b(S.)g(Gradsh)m(teyn)h (i)e(I.)h(M.)h(Ryzhik)f(\(ur.\),)h Fq(T)-7 b(able)36 b(of)i(Inte)-5 b(gr)g(als,)38 b(Series)f(and)g(Pr)-5 b(o)g(ducts)p Ft(,)458 3569 y(Academic)32 b(Press,)i(New)g(Y)-8 b(ork,)32 b(1980.)257 3833 y([23])49 b(T.)35 b(Kaluza,)g Fq(Sitzungsb)-5 b(er.)36 b(Pr)-5 b(euss)38 b(A)n(kad.)e(Wiss.)h(Berlin) f(Math.)h(Phys.)e Fu(B130)p Ft(,)h(\(1921\))458 4013 y(174;)i(O.)f(Klein,)f Fq(Z.)i(Phys.)f Fu(37)p Ft(,)h(\(1926\))d(895;)j (D.)f(Bailin)c(i)j(A.)h(Lo)m(w)m(e,)i Fq(R)-5 b(ep.)38 b(Pr)-5 b(o)g(g.)39 b(Phys)458 4194 y Fu(50)p Ft(,)33 b(\(1987\))e(1087.)257 4457 y([24])49 b(G.)f('t)h(Ho)s(oft,)j Fq(Salamfest)d(1993)p Ft(,)j(p.284,)g(gr-qc/9310026;)k(L.)48 b(Susskind,)107 b Fs(J.)49 b(Math.)458 4638 y(Ph)m(ys.)34 b Fu(36)f Ft(\(1995\))e(6377.)257 4901 y([25])49 b(H.-c.)33 b(Kao,)f(K.)g(Lee)h(i)f(T.)h(Lee,)66 b Fs(Ph)m(ys.)34 b(Rev.)f(D)f Fu(55)h Ft(\(1997\))e(6447.)257 5165 y([26])49 b(A.)d(P)-8 b(.)46 b(P)m(olyc)m(hronak)m(os,)99 b Fs(Ph)m(ys.)48 b(Lett.)e Fu(B264)f Ft(\(1991\))g(362;)51 b(T.)46 b(H.)g(Hansson,)k(J.) c(M.)458 5346 y(Leinaas)32 b(i)g(J.)g(Myrheim,)h Fs(Nucl.)f(Ph)m(ys.)j Fu(B384)d Ft(\(1992\))f(559.)p eop %%Page: 54 57 54 56 bop 257 -89 a Fs(LITERA)-8 b(TURA)2789 b Ft(54)257 294 y([27])49 b(L.)c(Brink,)i(T.)f(H.)f(Hansson,)k(S.)c(Konstein)f(i)g (M.)h(A.)g(V)-8 b(asiliev,)95 b Fs(Nucl.)44 b(Ph)m(ys.)j Fu(B401)458 474 y Ft(\(1993\))31 b(591.)257 734 y([28])49 b(S.)27 b(Iso,)57 b Fs(Mo)s(d.)27 b(Ph)m(ys.)i(Lett.)e Fu(A9)g Ft(\(1994\))f(2123;)i(H.)f(Azuma)g(i)f(S.)h(Iso,)57 b Fs(Ph)m(ys.)29 b(Lett.)e Fu(B331)458 914 y Ft(\(1994\))k(107.)257 1173 y([29])49 b(S.)33 b(Iso)g(i)e(S.)i(J.)g(Rey)-8 b(,)65 b Fs(Ph)m(ys.)35 b(Lett.)e Fu(B352)f Ft(\(1995\))f(111.)257 1433 y([30])49 b(S.)36 b(Iso,)g(D.)f(Karabali)e(i)i(B.)g(Sakita,)72 b Fs(Ph)m(ys.)38 b(Lett.)d Fu(B296)h Ft(\(1992\))e(143;)i(A.)g(Capp)s (eli,)f(C.)458 1613 y(A.)i(T)-8 b(rugen)m(b)s(erger)38 b(i)d(G.)h(R.)h(Zem)m(ba,)75 b Fs(Nucl.)36 b(Ph)m(ys.)i Fu(B396)f Ft(\(1993\))e(465)h(;)77 b Fs(Ph)m(ys.)39 b(Rev.)458 1794 y(Lett.)25 b Fu(72)g Ft(\(1994\))f(1902;)j(R.)e(Caracciolo,)g(A.)h (Lerda)f(i)f(G.)h(R.)g(Zem)m(ba,)53 b Fs(Ph)m(ys.)27 b(Lett.)e Fu(B352)458 1974 y Ft(\(1995\))31 b(304.)257 2234 y([31])49 b(T.)33 b(H.)g(Hansson,)g(J.)g(M.)g(Leinaas)f(i)g(J.)h (Myrheim,)64 b Fs(Nucl.)33 b(Ph)m(ys.)h Fu(B384)f Ft(\(1992\))e(559.) 257 2493 y([32])49 b(I.)33 b(Andri)m(\023)-46 b(c,)32 b(V.)h(Bardek)g(i)f(L.)g(Jonk)m(e,)67 b Fs(Fizik)-5 b(a)30 b Fu(B7)j Ft(\(1998\))e(119.)257 2752 y([33])49 b(R.)32 b(P)-8 b(.)33 b(Stanley)-8 b(,)33 b Fq(A)-5 b(dv.)35 b(Math.)d Fu(77)p Ft(,)h(\(1989\))e(76.)257 3011 y([34])49 b(J.)33 b(A.)f(Minahan)g(i)g(A.)h(P)-8 b(.)33 b(P)m(olyc)m(hronacos,)66 b Fs(Ph)m(ys.)34 b(Rev.)g Fu(B50)e Ft(\(1994\))f(4236.)257 3271 y([35])49 b(R.)e(F.)f(Streater)i(i)d(A.)j(S.)f(Wigh)m(tman,)i Fq(PCT,)f(Spin)f(and)g(Statistics,)52 b(and)47 b(A)n(l)5 b(l)48 b(That)p Ft(,)458 3451 y(The)24 b(Benjamin/Cummings)c (Publishing)h(Compan)m(y)-8 b(,)25 b(Inc.,)h(Adv)-5 b(anced)24 b(Bo)s(ok)f(Program,)458 3632 y(Reading,)32 b(Massac)m(h)m(usetts,)k (1964.)257 3891 y([36])49 b(I.)33 b(Andri)m(\023)-46 b(c,)32 b(V.)h(Bardek)g(i)f(L.)g(Jonk)m(e,)67 b Fs(Ph)m(ys.)34 b(Lett.)f Fu(B357)f Ft(\(1995\))g(374.)257 4150 y([37])49 b(J.)32 b(Maldacena,)h Fq(A)-5 b(dv.)34 b(The)-5 b(or.)34 b(Math.)h(Phys.)e Fu(2)p Ft(,)f(\(1998\))f(231;)h(O.)g(Aharon)m(y)-8 b(,)34 b(S.)e(Gusb)s(er,)458 4331 y(J.)h(Maldacena,)f(H.)h(OOguri)e(i)h (Y.)g(Oz,)h(hep-th/9905111.)257 4590 y([38])49 b(E.)25 b(Witten,)h Fq(A)-5 b(dv.)27 b(The)-5 b(or.)27 b(Math.)g(Phys.)e Fu(2)p Ft(,)h(\(1998\))e(505;)i(A.)f(M.)g(P)m(oly)m(ak)m(o)m(v,)i Fq(Int.)g(J.)h(Mo)-5 b(d.)458 4771 y(Phys.)40 b Fu(A14)p Ft(,)h(\(1999\))e(645;)k(I.)d(R.)g(Klebano)m(v)g(i)f(A.)h(A.)g (Tseytlin,)83 b Fs(Nucl.)40 b(Ph)m(ys.)i Fu(B546)458 4951 y Ft(\(1999\))31 b(155.)257 5210 y([39])49 b(N.)40 b(Ka)m(w)m(ak)-5 b(ami)39 b(i)g(S.-K.)h(Y)-8 b(ang,)84 b Fs(Ph)m(ys.)42 b(Rev.)e(Lett.)h Fu(67)f Ft(\(1991\))f(2493)g(;)44 b Fq(Pr)-5 b(o)g(g.)41 b(The)-5 b(or.)458 5391 y(Phys.)35 b(Suppl.)d Fu(107)p Ft(,)g(\(1992\))g(59.)p eop %%Page: 55 58 55 57 bop 257 -89 a Fs(LITERA)-8 b(TURA)2789 b Ft(55)257 294 y([40])49 b(Y.)34 b(Hatsugai,)g(M.)g(Kohmoto)f(i)g(Y.-)g(S.)i(W)-8 b(u,)34 b Fq(Pr)-5 b(o)g(g.)36 b(The)-5 b(or.)36 b(Phys.)g(Suppl.)d Fu(107)p Ft(,)i(\(1992\))458 474 y(101,)d(i)f(tamo)h(na)m(v)m(edena)i (literatura.)p eop %%Page: 56 59 56 58 bop 257 1082 a Fv(Sa)-6 b(\024)-110 b(zetak)257 1595 y Ft(U)32 b(radu)g(je)f(izlo)m(\024)-46 b(zena)31 b(k)m(olektivna)g(form)m(ulacija)e(Calogero-Sutherlando)m(v)m(og)h(i)h (Jac)m(kiw-Pi)g(mo-)257 1776 y(dela.)42 b(Nad)p 641 1723 31 4 v(ene)31 b(su)f(disp)s(erzione)f(relacije)f(malih)f(kv)-5 b(an)m(tnih)29 b(\015uktuacija)g(ok)m(o)h(o)s(dred)p 3332 1723 V(enih)f(rje)-5 b(\024)-44 b(se-)257 1956 y(nja)24 b(minimalne)d(energije)j(u)h(oba)f(mo)s(dela.)39 b(Uo)m(\024)-46 b(ceno)25 b(je)f(da)h(k)m(olektivna)f(teorija)f(p)s(olja,)i(o)s(dnosno) 257 2137 y(limes)33 b Fm(N)41 b Fp(!)31 b(1)j Ft(priro)s(dno)f(v)m(o)s (di)h(na)g(dimenzijsku)g(reduk)m(ciju)i(Jac)m(kiw-Pi)e(mo)s(dela,)28 b(\024)-44 b(sto)34 b(omo-)257 2317 y(gu)m(\023)-46 b(cuje)44 b(iden)m(ti\014k)-5 b(aciju)43 b(v)m(eze)i(med)p 1529 2265 V(u)e(mo)s(delima.)73 b(Diskutirane)43 b(su)h(p)s(osljedice)f (dimenzijsk)m(e)257 2498 y(reduk)m(cije,)34 b(statisti)m(\024)-46 b(ck)-5 b(a)31 b(transm)m(utacija)h(i)f(relacije)h(dualnosti.)1980 5674 y(56)p eop %%Page: 57 60 57 59 bop 257 1082 a Fv(Summary)257 1595 y Ft(W)-8 b(e)27 b(consider)f(the)g(Calogero-Sutherland)e(mo)s(del)g(and)i(the)g(Jac)m (kiw-Pi)g(mo)s(del)e(in)h(the)h(collecti-)257 1776 y(v)m(e-\014eld)32 b(approac)m(h)g(based)g(on)f(the)h(1)p Fm(=)-5 b(N)41 b Ft(expansion.)j(Disp)s(ersion)30 b(relations)g(for)g(small)g(quan-) 257 1956 y(tum)44 b(\015uctuations)h(around)f(sp)s(eci\014c)h (ground-state)f(solutions)g(ha)m(v)m(e)i(b)s(een)f(found)f(in)g(b)s (oth)257 2137 y(mo)s(dels.)74 b(It)43 b(has)h(b)s(een)f(noticed)g(that) g(collectiv)m(e-\014eld)e(theory)-8 b(,)47 b(i.)74 b(e.,)46 b(the)d(large-)p Fm(N)52 b Ft(limit,)257 2317 y(leads)32 b(to)g(the)h(dimensional)c(reduction)k(of)e(the)i(Jac)m(kiw-Pi)f(mo)s (del,)e(allo)m(wing)g(one)i(to)g(iden)m(tify)257 2498 y(the)j(t)m(yp)s(e)g(of)e(relation)f(b)s(et)m(w)m(een)k(the)e(t)m(w)m (o)h(mo)s(dels.)46 b(The)35 b(consequences)i(of)d(the)g(dimensional)257 2679 y(reduction,)26 b(b)s(eing)c(statistical)f(transm)m(utation)h(and) h(dualit)m(y)g(relations,)g(ha)m(v)m(e)i(b)s(een)f(discussed.)1980 5674 y(57)p eop %%Page: 58 61 58 60 bop 270 1033 a Fv(\024)257 1082 y(Ziv)-6 b(otopis)257 1595 y Ft(Ro)s(d)p 400 1543 31 4 v(ena)26 b(sam)f(27.)41 b(listopada)24 b(1970.)41 b(go)s(dine)25 b(u)h(Zagrebu,)h(gdje)f(sam)f (za)m(vr)-5 b(\024)-44 b(sila)26 b(osno)m(vn)m(u)h(i)e(sred-)257 1776 y(nju)31 b(\024)-44 b(sk)m(olu)37 b(\(MIOC\).)g(Go)s(dine)d(1988.) 53 b(upisala)35 b(sam)g(se)i(na)f(studij)g(\014zik)m(e)g(na)g(Priro)s (doslo)m(vno-)257 1956 y(matemati)m(\024)-46 b(ck)m(om)31 b(fakultetu)h(Sv)m(eu)m(\024)-46 b(cili)-5 b(\024)-44 b(sta)32 b(u)g(Zagrebu.)404 2137 y(Dana)43 b(21.)79 b(o)m(\024)-46 b(zujk)-5 b(a)45 b(1994.)78 b(usp)5 b(je)-5 b(\024)-44 b(sno)46 b(sam)e(p)s(olo)m(\024)-46 b(zila)41 b(diplomski)i(ispit)g(i)g (time)g(za)m(vr)-5 b(\024)-44 b(sila)257 2317 y(do)s(diplomski)47 b(studij)h(\014zik)m(e)i(na)f(Priro)s(doslo)m(vno-matemati)m(\024)-46 b(ck)m(om)45 b(fakultetu)j(u)h(Zagrebu)g(s)257 2498 y(prosje)m(\024)-46 b(cnom)51 b(o)s(cjenom)f(4.55.)97 b(Diplomski)48 b(rad,)55 b(s)c(temom)f("Nerelativisti)m(\024)-46 b(ck)-5 b(a)48 b(kv)-5 b(an)m(tna)52 b(i)257 2679 y(klasi)m(\024)-46 b(cna)49 b(Chern-Simonso)m(v)-5 b(a)50 b(teorija",)j(izradila)47 b(sam)i(p)s(o)s(d)h(v)m(o)s(dstv)m(om)g(prof.)96 b(dr.)f(Ivice)257 2859 y(Picek)-5 b(a)41 b(\(Fizi)m(\024)-46 b(cki)40 b(o)s(djel,)i (PMF\),)f(te)h(stru)m(\024)-46 b(cnim)40 b(v)m(o)s(dstv)m(om)i(dr.)70 b(V)-8 b(elimira)37 b(Bardek)-5 b(a)42 b(\(Za)m(v)m(o)s(d)257 3040 y(za)33 b(teorijsku)g(\014ziku,)g(IRB\).)404 3220 y(U)h(tra)m(vnju)g(iste)g(go)s(dine)e(zap)s(oslena)i(sam)f(na)h (Institutu)g(Rud)p 2688 3168 V(er)g(Bo)-5 b(\024)-44 b(sk)m(o)m(vi)m(\023)e(c,)35 b(u)f(Za)m(v)m(o)s(du)h(za)257 3401 y(teorijsku)41 b(\014ziku,)i(k)-5 b(ao)40 b(znanstv)m(eni)i(no)m (v)-5 b(ak.)68 b(Magistrirala)37 b(sam)j(21.)67 b(o)m(\024)-46 b(zujk)-5 b(a)41 b(1997.)66 b(i)40 b(time)257 3581 y(za)m(vr)-5 b(\024)-44 b(sila)32 b(p)s(oslijediplomski)d(studij)j(priro)s(dnih)f (znanosti)h(na)h(Priro)s(doslo)m(vno-matemati)m(\024)-46 b(ck)m(om)257 3762 y(fakultetu)22 b(u)g(Zagrebu.)39 b(Magistarski)21 b(rad,)j(s)e(temom)f("Solitoni)d(u)k(Calogero-Sutherlando)m(v)m(om)257 3943 y(mo)s(delu",)h(izradila)c(sam)i(p)s(o)s(d)g(v)m(o)s(dstv)m(om)i (dr.)40 b(V)-8 b(elimira)18 b(Bardek)-5 b(a)22 b(\(Za)m(v)m(o)s(d)g(za) f(teorijsku)h(\014ziku,)257 4123 y(IRB\).)1980 5674 y(58)p eop %%Page: 59 62 59 61 bop 257 1082 a Fv(P)-6 b(opis)77 b(rado)-6 b(v)-13 b(a)257 1595 y Ft(Znanstv)m(eni)33 b(rado)m(vi:)377 1838 y(1.)48 b(Quan)m(tum)27 b(\015uctuations)g(of)f(the)h(Chern-Simons)g (theory)g(and)g(dynamical)e(dimensional)501 2019 y(reduction,)501 2199 y(I.)33 b(Andri)m(\023)-46 b(c,)33 b(V.)f(Bardek,)i(L.)e(Jonk)m (e,)i(Ph)m(ys.)45 b(Rev.)f(D59)32 b(\(1999\))g(107702)377 2451 y(2.)48 b(Edge)33 b(excitations)f(and)h(the)g(con)m(tact)g(term)f (in)g(an)m(y)m(onic)h(systems,)501 2632 y(I.)g(Andri)m(\023)-46 b(c,)33 b(V.)f(Bardek,)i(L.)e(Jonk)m(e,)i(Nuo)m(v)m(o)g(Cim.)42 b(B113)32 b(\(1998\))f(1253)377 2884 y(3.)48 b(Collectiv)m(e-\014eld)27 b(\015uctuations)h(around)g(the)h(w)m(all)d(solution)h(of)g(the)i (Chern-Simons)f(the-)501 3065 y(ory)-8 b(,)501 3245 y(I.)33 b(Andri)m(\023)-46 b(c,)33 b(V.)f(Bardek,)i(L.)e(Jonk)m(e,)i(Fizik)-5 b(a)31 b(B7)h(\(1998\))g(119)377 3498 y(4.)48 b(Multi-v)m(ortex)32 b(solution)f(in)h(the)h(Sutherland)g(mo)s(del,)501 3678 y(I.)g(Andri)m(\023)-46 b(c,)33 b(V.)f(Bardek,)i(L.)e(Jonk)m(e,)i(J.)f (Ph)m(ys.)45 b(A30)32 b(\(1997\))g(717)377 3930 y(5.)48 b(Collectiv)m(e-Field)30 b(Excitations)i(in)g(the)h(Calogero)e(Mo)s (del,)501 4111 y(I.)i(Andri)m(\023)-46 b(c,)33 b(V.)f(Bardek,)i(L.)e (Jonk)m(e,)i(Fizik)-5 b(a)31 b(B4)h(\(1995\))g(93)377 4363 y(6.)48 b(Solitons)31 b(in)h(the)h(Calogero-Sutherland)e (Collectiv)m(e-Field)f(Mo)s(del,)501 4544 y(I.)j(Andri)m(\023)-46 b(c,)33 b(V.)f(Bardek,)i(L.)e(Jonk)m(e,)i(Ph)m(ys.)45 b(Lett.)f(B357)32 b(\(1995\))f(374)257 4787 y(Rado)m(vi)h(u)h(zb)s (ornicima:)377 5030 y(1.)48 b(Dimensional)30 b(Reduction)i(of)g(the)h (Chern-Simons)f(Theory)i(in)e(Large-N)g(Limit,)501 5210 y(I.)43 b(Andri)m(\023)-46 b(c,)45 b(V.)e(Bardek,)k(L.)42 b(Jonk)m(e,)47 b(Pro)s(ceedings)c(of)f(the)h(IV)g(W)-8 b(orkshop)44 b(on)f(QCD,)501 5391 y(P)m(aris)33 b(1998,)e(ur:)44 b(H.)33 b(M.)g(F)-8 b(ried)31 b(i)h(B.)h(Mueller,)f(W)-8 b(orld)31 b(Scien)m(ti\014c)i(1999,)f(str.)43 b(326-331)1980 5674 y(59)p eop %%Page: 60 63 60 62 bop 257 -89 a Fs(POPIS)34 b(RADO)m(V)-11 b(A)2687 b Ft(60)377 294 y(2.)48 b(Solitons)31 b(in)h(the)h(Calogero-Sutherland) e(Collectiv)m(e-Field)f(Mo)s(del,)501 474 y(I.)40 b(Andri)m(\023)-46 b(c,)42 b(V.)e(Bardek,)i(L.)e(Jonk)m(e,)j(Pro)s(ceedings)e(of)e(the)h (Sc)m(hladming)e(Sc)m(ho)s(ol)i(1995)501 655 y(\(Lecture)j(Notes)f(in)e (Ph)m(ysics)j(469\),)g(ur:)61 b(H.)42 b(Grosse)f(i)g(L.)g(Pittner,)j (Springer-V)-8 b(erlag)501 835 y(1996,)32 b(str.)44 b(245-248)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF