Thirring Model in Lower Dimensions: Nonperturbative Approaches

TL;DR

This paper reviews nonperturbative approaches to the Thirring model in lower dimensions, reformulating it as a gauge theory and analyzing mass generation phenomena in (2+1) dimensions.

Contribution

It presents a gauge theory reformulation of the Thirring model and demonstrates dynamical fermion mass generation using Schwinger-Dyson equations in (2+1) dimensions.

Findings

Reproduces bosonization of the massless Thirring model in (1+1) dimensions.

Shows dynamical fermion mass generation in (2+1) dimensions for N < 128/3π².

Abstract

A reformulation of the Thirring model as a gauge theory on both continuum spacetime and discretized lattice is reviewed. In (1+1) dimensions, our result reproduces consistently the bosonization of the massless Thirring model. In (2+1) dimensions, the analysis by use of Schwinger-Dyson equation is shown to exhibit dynamical fermion mass generation when the number $N$ of four-component fermions is less than the critical value $N_{cr}= 128/3\pi^{2}$.