The D-Gauge: a solution to the i-r problem for fermion mass generation in QED3 in the Matsubara formalism

TL;DR

This paper addresses infrared divergences in the Schwinger-Dyson approach to fermion mass generation in QED3 at finite temperature by introducing a non-local gauge and a specific vertex ansatz, enabling finite calculations of the mass function.

Contribution

It proposes a new gauge choice and vertex ansatz that eliminate infrared divergences, allowing for a consistent calculation of the physical mass in QED3 at finite temperature.

Findings

The physical mass M can be calculated without infrared divergences.

The constant mass approximation M=M(0,pi T) is justified at finite temperature.

The ratio r remains close to previous estimates, validating earlier results.

Abstract

A serious problem with the Schwinger-Dyson approach to dynamical mass generation in QED3 at finite temperature is that the contribution from the transverse part of the photon propagator, in the Landau gauge, leads to infrared divergences in both the mass function and the wavefunction renormalisation. We show how, by using a simple choice of vertex anatz and a choice of non-local gauge (the `D-gauge') both quantities can be made finite. We formulate an equation for the physical mass M. and show that it reduces to the coresponding equation obtained in the constant physical mass approximation M=M(0,pi T) (which is finite). There for at finite temperature, we are able to justify a `constant' mass approximation for M, and show that the value of r (the ratio of twice the physical mass at zero temperature to the critical temperature) remains close to the value obtained in previous calculations with retardation.