Fermion Mass Generation in the D-dimensional Thirring Model as a Gauge Theory

TL;DR

This paper investigates fermion mass generation in a D-dimensional Thirring model by solving the Schwinger-Dyson equation, deriving explicit formulas for the dynamical mass and critical line, and confirming results numerically in 2+1 dimensions.

Contribution

It provides an analytical solution for fermion mass and critical behavior in the D-dimensional Thirring model as a gauge theory, supported by numerical verification.

Findings

Explicit form of dynamical fermion mass derived

Critical line in (N,1/g) space identified

Numerical confirmation in 2+1 dimensions

Abstract

Based on the Schwinger-Dyson (SD) equation, the fermion mass generation is further studied in the D(2<D<4)-dimensional Thirring model as a gauge theory previously proposed. By using a certain approximation to the kernel, we analytically obtained explicit form of the dynamical mass of fermion and the critical line in (N,1/g) space, where N is the number of fermions and g is the dimensionless vector-type four-fermion coupling constant. This analytical result is confirmed by the numerical solution for the SD equation with exact form of the kernel in (2+1) dimensions.