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Equation of state of a meson gas from the PNJL model for interacting quarks

We compute the equation of state of hadronic matter at finite temperature with zero net baryon density by the Nambu-Jona-Lasinio model for interacting quarks in uniform background temporal color gauge fields. In the low temperature confining phase, unphysical thermal quark-antiquark excitations which would appear in the mean field approximation, are eliminated by enforcing vanishing expectation value of the "Polyakov-loop" of the background gauge field, while in the high temperature confining phase this expectation value is taken as close to unity allowing thermal excitations of free quarks and antiquarks. Mesonic excitations in the low temperature phase appear in the correlation energy as contributions of collective excitations. We describe them in terms of thermal fluctuations of auxiliary fields in one-loop (Gaussian) approximation, where pions appear as Nambu-Goldstone modes associated with dynamical symmetry breaking of the chiral symmetry in the limit of vanishing bare quark masses. We show that the equations of state reduces to that of free meson gas with numerically small corrections arising from the composite nature of mesons.