  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.

High Energy Physics - Theory