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We complete the derivation of the Cornwall-Jackiw-Tomboulis effectivepotential for quark propagator at finite temperature and finite quark chemicalpotential in the real-time formalism of thermal field theory and in Landaugauge. In the approximation that the function $A(p^2)$ in inverse quarkpropagator is replaced by unity, by means of the running gauge coupling and thequark mass function invariant under the renormalization group in zerotemperature Quantum Chromadynamics (QCD), we obtain a calculable expression forthe thermal effective potential which will be a useful means to research chiralphase transition in QCD in the real-time formalism.Comment: 5 pages, Latex, no figur

Cornwall–Jackiw–Tomboulis Effective Potential for Quark Propagator in Real-Time Thermal Field Theory and Landau Gauge