Cornwall–Jackiw–Tomboulis Effective Potential for Quark Propagator inReal-Time Thermal Field Theory and Landau Gauge**The project supported byNational Natural Science Foundation of China

Abstract

We complete the derivation of the Cornwall–Jackiw–Tombouliseffective potential for quark propagator at finite temperature andfinite quark chemical potential in the real-time formalism ofthermal field theory and in Landau gauge. In the approximationthat the function A(p2) in inverse quark propagator is replacedby unity, by means of the running gauge coupling and the quarkmass function invariant under the renormalization group in zerotemperature Quantum Chromadynamics (QCD), we obtain a calculableexpression for the thermal effective potential, which will be auseful means to research chiral phase transition in QCD in thereal-time formalism.