Phase Structure of Thermal QCD/QED:A Gauge Invariant Solution of the HTL Resummed Improved Ladder Dyson-Schwinger Equation

TL;DR

This paper develops a gauge-invariant method for solving the Dyson-Schwinger equation in thermal QCD/QED using HTL resummation, providing numerical results and analyzing the properties of these solutions.

Contribution

It introduces a procedure to obtain gauge-invariant solutions of the Dyson-Schwinger equation satisfying Ward-Takahashi identity in thermal QCD/QED.

Findings

Numerical solutions demonstrate gauge invariance.

Properties of gauge-invariant solutions are characterized.

The method ensures consistency with Ward-Takahashi identity.

Abstract

Based on the hard-thermal-loop resummed improved ladder Dyson-Schwinger quation for the fermion mass function, we propose a procedure how we can get the gauge invariant solution in the sense it satisfies the Ward-Takahashi identity. Results of the numerical analysis are shown and properties of the ``gauge-invariant'' solutions are discussed.