Renormalization in self-consistent approximation schemes at finite temperature. III. Global symmetries

Hendrik van Hees and Jörn Knoll
Phys. Rev. D 66, 025028 – Published 31 July 2002
PDFExport Citation

Abstract

We investigate the symmetry properties for Baym’s Φ-derivable schemes. We show that in general the solutions of the dynamical equations of motion, derived from approximations of the Φ functional, do not satisfy the Ward-Takahashi identities of the symmetry of the underlying classical action, although the conservation laws for the expectation values of the corresponding Noether currents are satisfied exactly for the approximation. Further we prove that one can define an effective action functional in terms of the self-consistent propagators which is invariant under the operation of the same symmetry group representation as the classical action. The requirements for this theorem to hold true are the same as for perturbative approximations: The symmetry has to be realized linearly on the fields and it must be free of anomalies; i.e., there should exist a symmetry-conserving regularization scheme. In addition, if the theory is renormalizable in Dyson’s narrow sense, it can be renormalized with counterterms which do not violate the symmetry.

  • Received 1 March 2002

DOI:https://doi.org/10.1103/PhysRevD.66.025028

©2002 American Physical Society

Authors & Affiliations

Hendrik van Hees

  • Fakultät für Physik, Universität Bielefeld, Universitätsstraße, D-33615 Bielefeld, Germany

Jörn Knoll

  • GSI Darmstadt, Planckstraße 1, D-64291 Darmstadt, Germany

References (Subscription Required)

Click to Expand
Issue

Vol. 66, Iss. 2 — 15 July 2002

Reuse & Permissions
Access Options

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×