Infrared divergence in QED$_3$ at finite temperature

TL;DR

This paper investigates the infrared divergence in finite-temperature QED3, analyzing how the photon propagator affects the dynamically generated fermion mass and establishing conditions on cutoff parameters for physical consistency.

Contribution

It introduces a phenomenological approach to handle infrared divergence in QED3 at finite temperature by incorporating both photon propagator parts and analyzing their effects on fermion mass.

Findings

The ratio 2*Mass(T=0)/critical temperature is approximately 6.

Infrared divergence is likely an artifact of leading order approximation.

Conditions on cutoff parameters are derived for physical consistency.

Abstract

We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour $QED_{3}$ at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artefact of taking into account only the leading order term in the $1 \over N$ expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger-Dyson equation we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio $r=2*Mass(T=0)/critical temperature$ is approximately 6, consistently with previous calculations which neglected the transverse photon contribution.