Naslov
Scalar Field Theory on Non-commutative Snyder Space-Time

Autori
Battisti, Marco Valerio ; Meljanac, Stjepan

Izvornik
Physical Review D - Particles, Fields, Gravitation, and Cosmology (1550-7998) 82 (2010); 024028-024037

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

Ključne riječi
noncommutative field theory; snyder space-time

Sažetak
We construct a scalar field theory on the Snyder non-commutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincar\'e algebra is undeformed. The Lorentz sector is undeformed at both algebraic and co-algebraic level, but the co-product for momenta (defining the star-product) is non-co-associative. The Snyder-deformed Poincar\'e group is described by a non-co-associative Hopf algebra. The definition of the interacting theory in terms of a non-associative star-product is thus questionable. We avoid the non-associativity by the use of a space-time picture based on the concept of realization of a non-commutative geometry. The two main results we obtain are: (i) the generic (namely for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a non-ambiguous self interacting scalar field theory on this space-time. The first order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.

Izvorni jezik
Engleski

Znanstvena područja
Fizika

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