Renormalization in self-consistent approximation schemes at finite temperature: Theory

Hendrik van Hees and Jörn Knoll
Phys. Rev. D 65, 025010 – Published 26 December 2001
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Abstract

Within finite temperature field theory, we show that truncated nonperturbative self-consistent Dyson resummation schemes can be renormalized with local counterterms defined at the vacuum level. The requirements are that the underlying theory is renormalizable and that the self-consistent scheme follows Baym’s Φ-derivable concept. The scheme generates both the renormalized self-consistent equations of motion and the closed equations for the infinite set of counterterms. At the same time the corresponding two-particle irreducible generating functional and the thermodynamical potential can be renormalized, consistent with the equations of motion. This guarantees that the standard Φ-derivable properties such as thermodynamic consistency and exact conservation laws hold also for the renormalized approximation schemes. The proof uses the techniques of Bogoliubov-Parasiuk-Hepp-Zimmermann renormalization to cope with the explicit and the hidden overlapping vacuum divergences.

  • Received 18 July 2001

DOI:https://doi.org/10.1103/PhysRevD.65.025010

©2001 American Physical Society

Authors & Affiliations

Hendrik van Hees and Jörn Knoll

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

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Issue

Vol. 65, Iss. 2 — 15 January 2002

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