Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1999-11-24
Phys.Rev. D61 (2000) 105002
Physics
High Energy Physics
High Energy Physics - Phenomenology
31 pages with 7 eps figures
Scientific paper
10.1103/PhysRevD.61.105002
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.
Aarts Gert
Nauta Bert-Jan
van Weert Chris G.
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