Naslov
The energy operator for a model with a multiparametric infinite statistics

Autori
Meljanac, Stjepan ; Perica, Ante ; Svrtan, Dragutin

Izvornik
Journal of physics. A, mathematical and general (0305-4470) 36 (2003); 6337-6349

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
infinite statistics; multiparametric deformations; quantum algebras

Sažetak
In this paper we consider energy operator (a free Hamiltonian), in the second-quantized approach, for the multiparameter quon algebras: $a_{; ; ; i}; ; ; a_{; ; ; j}; ; ; ^{; ; ; \dagger}; ; ; -q_{; ; ; ij}; ; ; a_{; ; ; j}; ; ; ^{; ; ; \dagger}; ; ; a_{; ; ; i}; ; ; = \delta_{; ; ; ij}; ; ; , i, j\in I$ with $(q_{; ; ; ij}; ; ; )_{; ; ; i, j\in I}; ; ; $ any hermitian matrix of deformation parameters. We obtain an elegant formula for normally ordered (sometimes called Wick-ordered) series expansions of number operators (which determine a free Hamiltonian). As a main result (see Theorem 1) we prove that the number operators are given, with respect to a basis formed by "generalized Lie elements", by certain normally ordered quadratic expressions with coefficients given precisely by the entries of the inverses of Gram matrices of multiparticle weight spaces. (This settles a conjecture of two of the authors (S.M and A.P), stated in [8]). These Gram matrices are hermitian generalizations of the Varchenko's matrices, associated to a quantum (symmetric) bilinear form of diagonal arrangements of hyperplanes (see [12]). The solution of the inversion problem of such matrices in [9] (Theorem 2.2.17), leads to an effective formula for the number operators studied in this paper. The one parameter case, in the monomial basis, was studied by Zagier [15], Stanciu [11] and M&oslash ; ; ; ; ller [6].

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Fizika

POVEZANOST RADA