Annales Henri Poincaré

, Volume 2, Issue 2, pp 387–402

Temperature Independent Renormalization of Finite Temperature Field Theory

  • Christoph Kopper
  • Volkhard Müller
  • Thomas Reisz

DOI: 10.1007/PL00001039

Cite this article as:
Kopper, C., Müller, V. & Reisz, T. Ann. Henri Poincaré (2001) 2: 387. doi:10.1007/PL00001039


We analyze 4-dimensional massive \( \varphi^4 \) theory at finite temperature T in the imaginary-time formalism. We present a rigorous proof that this quantum field theory is renormalizable, to all orders of the loop expansion. Our main point is to show that the counterterms can be chosen temperature independent, so that the temperature flow of the relevant parameters as a function of T can be followed. Our result confirms the experience from explicit calculations to the leading orders. The proof is based on flow equations, i.e. on the (perturbative) Wilson renormalization group. In fact we will show that the difference between the theories at T > 0 and at T = 0 contains no relevant terms. Contrary to BPHZ type formalisms our approach permits to lay hand on renormalization conditions and counterterms at the same time, since both appear as boundary terms of the renormalization group flow. This is crucial for the proof.

Copyright information

© Birkhäuser Verlag Basel, 2001

Authors and Affiliations

  • Christoph Kopper
    • 1
  • Volkhard Müller
    • 2
  • Thomas Reisz
    • 3
  1. 1.Centre de Physique Théorique, Ecole Polytechnique, F-91128 Palaiseau, France, e-mail: kopper@cpht.polytechnique.frFR
  2. 2.Fachbereich Physik, Universität Kaiserslautern, D-67653 Kaiserslautern, Germany, e-mail: vfm@physik.uni-kl.deDE
  3. 3.Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany, e-mail: reisz@thphys.uni-heidelberg.deDE
  4. 4.Service de Physique Théorique de Saclay, CE-Saclay, F-91191 Gif-sur-Yvette Cedex, FranceFR

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