Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O(N) symmetry

Yu. B. Ivanov, F. Riek, H. van Hees, and J. Knoll
Phys. Rev. D 72, 036008 – Published 23 August 2005

Abstract

The renormalization of a gapless Φ-derivable Hartree-Fock approximation to the O(N)-symmetric λϕ4 theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper [Yu. B. Ivanov, F. Riek, and J. Knoll, Phys. Rev. D 71, 105016 (2005).] in order to preserve all the desirable features of Φ-derivable Dyson-Schwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) while simultaneously restoring the Nambu-Goldstone theorem in the broken phase. It is shown that unlike for the conventional Hartree-Fock approximation this approach allows for a scale-independent renormalization in the vacuum. However, the scale dependence still persists at finite temperatures. Various branches of the solution are studied. The occurrence of a limiting temperature inherent in the renormalized Hartree-Fock approximation at fixed renormalization scale μ is discussed.

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  • Received 17 June 2005

DOI:https://doi.org/10.1103/PhysRevD.72.036008

©2005 American Physical Society

Authors & Affiliations

Yu. B. Ivanov1,2,*, F. Riek1,†, H. van Hees3,‡, and J. Knoll1,§

  • 1Gesellschaft für Schwerionenforschung mbH, Planckstrasse 1, D-64291 Darmstadt, Germany
  • 2Kurchatov Institute, Kurchatov Square 1, Moscow 123182, Russia
  • 3Cyclotron Institute, Texas A&M University, College Station, Texas 77843-3366, USA

  • *Electronic address: Y.Ivanov@gsi.de
  • Electronic address: F.Riek@gsi.de
  • Electronic address: hees@comp.tamu.edu
  • §Electronic address: J.Knoll@gsi.de

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Vol. 72, Iss. 3 — 1 August 2005

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