Infrared behavior of dynamical fermion mass generation in QED$_{3}$

TL;DR

This paper investigates how finite temperature and disorder affect dynamical fermion mass generation in QED3, introducing a new approximation that avoids infrared divergence and aligns with zero-temperature results.

Contribution

It develops a novel approximation method incorporating energy-dependent gauge boson propagator to study dynamical mass generation at finite temperature.

Findings

Infrared divergence appears under the instantaneous approximation at finite temperature.

The new approximation eliminates infrared divergence in the dynamical fermion mass.

Results are consistent with established zero-temperature findings.

Abstract

Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing to the well-established results obtained at zero temperature.