Real-time thermal Schwinger-Dyson equation for quark self-energy in Landau gauge

TL;DR

This paper derives a real-time thermal Schwinger-Dyson equation for quark self-energy in Landau gauge, providing a simplified approach for studying chiral symmetry phase transitions at finite temperature and chemical potential.

Contribution

The paper introduces a formal derivation of the thermal Schwinger-Dyson equation for quark propagator in Landau gauge, with an approximation applicable below a specific infrared cutoff.

Findings

A feasible approximation of the inverse quark propagator as $A(p^2)=1$ for $T < p_c$

Derivation of the real-time thermal Schwinger-Dyson equation at finite temperature and chemical potential

Application to chiral symmetry phase transition analysis in QCD

Abstract

By means of a formal expression of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential, we derive the real-time thermal Schwinger-Dyson equation for quark propagator in Landau gauge. Denote the inverse quark propagator by $A(p^2)\not{p}-B(p^2)$, we argue that, when temperature $T$ is less than the given infrared momentum cutoff $p_c$, $A(p^2)=1$ is a feasible approximation and can be assumed in discussions of chiral symmetry phase transition problem in QCD.