Hendrik van Hees (1) and Jörn Knoll (2)
(1) Fakultät für Physik, Universität Bielefeld
Universitätsstraße, D-33615 Bielefeld,
(2) GSI Darmstadt

 Renormalization and selfconsistency in quantum field theory

 Within  finite temperature  quantum field theory, we show that
 self-consistent Dyson resummation schemes can be renormalized with all
 counter terms defined at the vacuum level (1) provided that the
 underlying theory is renormalizable and that the self-consistent scheme
 follows Baym's  Phi-derivable concept. The scheme generates the
 renormalized self-consistent equations of motion and at the same time
 the corresponding generating functional and the thermodynamical
 potential in consistency with the equations of motion. This guarantees
 the standard  Phi-derivable properties like thermodynamic consistency
 and exact conservation laws also for the renormalized approximation
 schemes to hold true.

 First numerical applications for the simple phi^4-theory including the
 tadpole and the sunset self-energy diagram are presented in order to
 show the practicability of the scheme (2).

 The question of symmetry violations of such schemes and the concepts to
 recover the symmerties (like Goldstone modes) are discussed (3).

 (1) H. van Hees and J. Knoll, Phys. Rev. D 65, 025010 (2002)
     (hep-ph/ 0107200)
 (2) H. van Hees and J. Knoll, Phys. Rev. D 65 (2002) 105005
     (hep-ph/0111193)
 (3) H. van Hees and J. Knoll, Accepted for publication by Phys. Rev. D
     (hep-ph/0203008)