Renormalization in Self-Consistent Approximation schemes at Finite Temperature III: Global Symmetries

Abstract

We investigate the symmetry properties for Baym's $\Phi$-derivable schemes. We show that in general the solutions of the dynamical equations of motion, derived from approximations of the $\Phi$-functional, do not fulfill 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 fulfilled 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 counter terms which do not violate the symmetry.

32 papges, 3 figures, uses ReVTeX 4, V2: Added one more reference, V3: Corrected some typos, added two more sections about the large-N expansion

References in corpus (5)

• Controlled nonperturbative dynamics of quantum fields out of equilibrium
• Renormalization in Self-Consistent Approximations schemes at Finite Temperature I: Theory
• Renormalization of Self-consistent Approximation schemes Finite Temperature II: Applications to the Sunset Diagram
• Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory
• Exact Conservation Laws of the Gradient Expanded Kadanoff-Baym Equations

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