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

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.