ar X iv : h ep - p h / 02 10 26 2 v 2 4 N ov 2 00 2 RENORMALIZATION OF SELF - CONSISTENT Φ - DERIVABLE APPROXIMATIONS

Within finite temperature field theory, we show that truncated non-perturbative self-consistent Dyson resummation schemes can be renormalized with local vacuum counterterms. For this the theory has to be renormalizable in the usual sense and the self-consistent scheme must follow Baym's Φ-derivable concept. Our BPHZ-renormalization scheme leads to renormalized self-consistent equations of motion. At the same time the corresponding 2PI-generating functional and the thermodynamic potential can be renormalized with the same counterterms used for the equations of motion. This guarantees the standard Φ-derivable properties like thermodynamic consistency and exact conservation laws also for the renor-malized approximation schemes. We give also a short overview over symmetry properties of the various functions defined within the 2PI scheme for the case that the underlying classical field theory has a global linearly realized symmetry.