Chiral bosonization for non-commutative fields -: art. no. 022

A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to(1+theta(2)) where theta is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to c'=croot1+theta(2) where c is the speed of light. Lorentz invariance remains intact if c is rescaled by c-->c'. The dispersion relation for bosons and fermions, in this case, is given by omega=c'\k\.