Cornwall-Jackiw-Tomboulis effective potential for quark propagator in real-time thermal field theory and Landau gauge

TL;DR

This paper derives a calculable form of the Cornwall-Jackiw-Tomboulis effective potential for quark propagators at finite temperature and chemical potential in real-time thermal field theory, aiding the study of chiral phase transitions in QCD.

Contribution

It completes the derivation of the effective potential in real-time formalism and Landau gauge, using approximations and renormalization group invariance for practical calculations.

Findings

Derived a usable expression for the thermal effective potential in QCD.

Facilitates research on chiral phase transition in real-time formalism.

Provides a foundation for future non-perturbative studies in thermal QCD.

Abstract

We complete the derivation of the Cornwall-Jackiw-Tomboulis effective potential for quark propagator at finite temperature and finite quark chemical potential in the real-time formalism of thermal field theory and in Landau gauge. In the approximation that the function $A(p^2)$ in inverse quark propagator is replaced by unity, by means of the running gauge coupling and the quark mass function invariant under the renormalization group in zero temperature Quantum Chromadynamics (QCD), we obtain a calculable expression for the thermal effective potential which will be a useful means to research chiral phase transition in QCD in the real-time formalism.