Gauge Parameter Dependence of the 1-loop Fermion Self Energy at Finite Temperature

TL;DR

This paper investigates how the 1-loop fermion self energy at finite temperature depends on gauge parameters, revealing that the temperature-dependent term is gauge-dependent and drawing parallels with the ladder approximation Schwinger-Dyson equation.

Contribution

It demonstrates the gauge parameter dependence of the 1-loop fermion self energy at finite temperature and relates it to the ladder approximation Schwinger-Dyson equation.

Findings

Wave function renormalization constant approaches 1 with negative gauge parameter

Temperature dependence term shows gauge parameter dependence

Analogy with ladder approximation Schwinger-Dyson equation

Abstract

We show a gauge parameter dependence of the 1-loop fermion self energy at finite temperature before the analytic continuation. We also show a gauge parameter dependence of only the temperature dependence term. The result is the same as the ladder approximation Schwinger-Dyson equation. The wave function renormalization constant approaches 1 by taking a negative gauge parameter. The analogy of the ladder approximation Schwinger-Dyson equation and the 1-loop calculation will help the analysis of the phase transition.