Self-consistent approximations for field theories at finite temperature

Various mean field approximations at finite temperature are used for calculating ground state energies and propagators of the φ4 theory in two dimensions and quantum chromodynamics (QCD). In the case of the φ4 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. (author)