Thermodynamics of hadrons using the Gaussian functional method in the linear sigma model

We investigate thermodynamics of hadrons using the Gaussian functional method (GFM) at finite temperature. Since the interaction among mesons is very large, we take into account fluctuations of mesons around their mean field values using the GFM. We obtain the ground state energy by solving the Schrödinger equation. The meson masses are obtained using the energy minimization condition. The resulting mass of pion is not zero even in the spontaneous chiral symmetry broken phase due to the non-perturbative effect. We consider then the bound state of mesons using the Bethe-Salpeter equation and show that the Nambu-Goldstone theorem is recovered. We investigate further the behavior of the meson masses and the mean filed value as functions of temperature for the cases of chiral limit and explicit chiral symmetry breaking.