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By applying the closed-time-path Green function formalism to the chiraldynamical model based on an effective Lagrangian of chiral quarks with thenonlinear-realized meson fields as bosonized auxiliary fields, we then arriveat a chiral thermodynamic model for the meson fields with finite temperature.Particular attention is paid to the spontaneous chiral symmetry breaking andrestoration from the dynamically generated effective composite Higgs potentialof meson fields at finite temperature. It is shown that the minimal conditionof the effective composite Higgs potential of meson fields leads to thethermodynamic gap equation at finite temperature, which enables us toinvestigate the critical behavior of the effective chiral thermodynamical modeland to explore the QCD phase transition. After fixing the free parameters inthe effective chiral Lagrangian at low energies with zero temperature, wedetermine the critical temperature of the chiral symmetry restoration andpresent a consistent prediction for the thermodynamical behavior of severalphysically interesting quantities, which include the vacuum expectation value$v_o(T)$, quark condensate $<\bar{q}q>(T)$, pion decay constant $f_\pi(T)$ andpion meson mass $m_{\pi}(T)$. In particular, it is also shown that thethermodynamic scaling behavior of these quantities becomes the same near thecritical point of phase transition.

Chiral Thermodynamic Model of QCD and its Critical Behavior in the Closed-Time-Path Green Function Approach