Bosonization and the generalized Mandelstam operators

Abstract

The generalized massive Thirring model (GMT) with $N_f(=$number of positive roots of $su(n)$) fermion species is bosonized in the context of the functional integral and operator formulations and shown to be equivalent to a generalized sine-Gordon model (GSG) with $N_f$ interacting soliton species. The generalized Mandelstam-Halpern soliton operators are constructed and the fermion-boson mapping is established through a set of generalized bosonization rules in a quotient positive definite Hilbert space of states. Each fermion species is mapped to its corresponding soliton in the spirit of particle/soliton duality of Abelian bosonization. The examples of $su(3)$ and $su(4)$ are presented.

4 pages, LaTex. Talk presented at the V Latin American Symposium on High Energy Physics (V-SILAFAE), Lima Peru, July 12-17, 2004