Numerical Calculation of Schwinger-Dyson Equation with Momentum-Dependent Gauge Parameter at Finite Temperature

TL;DR

This paper numerically investigates chiral symmetry breaking at finite temperature via the Schwinger-Dyson equation, incorporating a momentum-dependent gauge parameter, and examines gauge invariance within the ladder approximation.

Contribution

It introduces a numerical method for solving the Schwinger-Dyson equation with a momentum-dependent gauge parameter at finite temperature, assessing gauge invariance.

Findings

Critical temperature similar to Landau gauge results

Gauge invariance approximately maintained in ladder approximation

Method confirms robustness of chiral symmetry breaking analysis

Abstract

Chiral symmetry at finite temperature is studied using the Schwinger-Dyson equation. We calculate numerically the critical temperature using the Schwinger-Dyson equation with the gauge parameter that depends on an external momentum. The critical temperature obtained by this method is similar to that with the Landau gauge and wave function renormalization constant 1. Moreover, the gauge invariance in the ladder approximation is examined using our method.