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Divergences in real-time classical field theories at nonzero temperature Institut fur theoretische Physik, Universitat Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
 

Summary: Divergences in real-time classical field theories at nonzero temperature
Gert Aarts
Institut fušr theoretische Physik, Universitašt Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
Bert-Jan Nauta and Chris G. van Weert
Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam, the Netherlands
Received 29 November 1999; published 12 April 2000
The classical approximation provides a non-perturbative approach to time-dependent problems in finite
temperature field theory. We study the divergences in hot classical field theory perturbatively. At one loop, we
show that the linear divergences are completely determined by the classical equivalent of the hard thermal
loops in hot quantum field theories, and that logarithmic divergences are absent. To deal with higher-loop
diagrams, we present a general argument that the superficial degree of divergence of classical vertex functions
decreases by one with each additional loop: one-loop contributions are superficially linearly divergent, two-
loop contributions are superficially logarithmically divergent, and three- and higher-loop contributions are
superficially finite. We verify this for two-loop SU(N) self-energy diagrams in Feynman and Coulomb gauges.
We argue that hot, classical scalar field theory may be completely renormalized by local mass counterterms,
and discuss renormalization of SU(N) gauge theories.
PACS number s : 11.10.Wx, 11.15.Kc
I. INTRODUCTION
The classical approximation 1 is a useful tool for the
study of infrared properties of quantum fields at high tem-

  

Source: Aarts, Gert - Department of Physics, University of Wales Swansea

 

Collections: Physics