Bosonization and the generalized Mandelstam operators

TL;DR

This paper extends bosonization techniques to the generalized massive Thirring model with multiple fermion species, establishing a duality with a generalized sine-Gordon model and constructing corresponding soliton operators.

Contribution

It introduces a generalized bosonization framework for the GMT model with multiple fermion species and constructs the generalized Mandelstam-Halpern soliton operators.

Findings

Fermion species are mapped to solitons in a generalized bosonization scheme.

The equivalence between GMT and GSG models is established.

Explicit examples for su(3) and su(4) are provided.

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.