Chiral fermion meson model at finite temperature

We study the chiral fermion meson model which is the well-known linear sigma model of Gell-Mann and Levy at finite temperature. A modified self-consistent resummation (MSCR) which resume higher order terms in the perturbative expansion is proposed. It is shown that with the MSCR the problem of tachyonic masses is solved, the renormalization of the gap equations is carried out, and Goldstone's theorem is verified. We also apply the method to investigate another known case at high temperature and compare with results found in the literature.