Chiral symmetry restoration and pion properties in a q-deformed NJL model

Abstract

We review the implementation of a q-deformed fermionic algebra in the Nambu-Jona-Lasinio model (NJL). The gap equations obtained from a deformed condensate as well as from the deformation of the NJL Hamiltonian are discussed. The effect of both temperature and deformation in the chiral symmetry restoration process as well as in the pion properties is studied.

Remarks on SU_q(2) fermions

“…( 11)-( 13) is an highly non-trivial problem. In the literature, where SU q (2) fermions were studied in statistical mechanics [33,35,36,37,38] and to QFT [39,40,41], it is assumed that…”

“…In particular, one can write down deformations of usual commutation (anticommutation) relations for bosons (fermion), which are invariant under linear transformations belonging to quantum groups as SU q (N ) [26,27,28,29], GL p,q (2) [30,31] and SU p,q (2) [31,32]. Noticeably, formulas connecting deformed boson and fermion operators with usual (undeformed) ones were derived [33,34], and applications to statistical mechanics [30,31,32,33,35,36,37,38] and quantum field theory (QFT) [39,40,41] were proposed. Probably, the most important application of SU q (N ) bosons is the derivation of the so-called generalized uncertainty principle (GUP) [42], which is a very active area of research [43,44,45].…”