Effect of retardation on dynamical mass generation in two-dimensional QED at finite temperature

TL;DR

This paper investigates how retardation effects influence dynamical mass generation in two-dimensional QED at finite temperature, showing that retardation reduces the mass-to-critical-temperature ratio and discussing the implications of including transverse photon contributions.

Contribution

It provides a leading-order evaluation of the photon polarization tensor with explicit retarded propagators and analyzes the impact of retardation on the fermion mass gap in finite-temperature QED.

Findings

Retardation decreases the mass ratio r from about 10 to 6.

The gap equation with frequency-dependent mass confirms r remains close to 6.

Discussion on including transverse propagator effects.

Abstract

The effect of retardation on dynamical mass generation in is studied, in the imaginary time formalism. The photon porarization tensor is evaluated to leading order in 1/N (N is the number of flavours), and simple closed form expressions are found for the fully retarded longitudinal and transverse propagators, which have the correct limit when T goes to zero. The resulting S-D equation for the fermion mass (at order 1/N) has an infrared divergence associated with the contribution of the transverse photon propagator; only the longitudinal contribution is retained, as in earlier treatments. For solutions of constant mass, it is found that the retardation reduces the value of the parameter r (the ratio of twice the mass to the critical temperature) from about 10 to about 6. The gap equation is then solved allowing for the mass to depend on frequency. It was found that the r value remained close to 6. Possibilities for including the transverse propagator are discussed.