Optimized perturbation theory at finite temperature

An optimized perturbation theory (OPT) at finite temperature $T,$ which resums higher order terms in the naive perturbation, is developed in O(N) φ⁴ theory. It is proved that (i) the renormalization of the ultraviolet divergences can be carried out systematically in any given order of OPT and (ii) the Nambu-Goldstone theorem is satisfied for arbitrary N and for any given order of OPT. The method is applied for the O(4) σ model to study the soft modes associated with the chiral transition in quantum chromodynamics. Threshold enhancement of the spectral functions at finite T in the scalar and pseudoscalar channels is shown to be a typical signal of the chiral transition.