Self-consistent approximations for field theories at finite temperature

Abstract

Various mean field approximations at finite temperature are used for calculating ground state energies and propagators of the [Formula: see text] theory in two dimensions and quantum chromodynamics (QCD). In the case of the [Formula: see text] theory a symmetry restoration is observed above a critical coupling constant if a temperature independent renormalization is used. In the case of QCD the mean field approximation is insufficient but can be regarded as a starting point for more complicated approximations, which are discussed qualitatively.