Foam Diagram Summation at Finite Temperature

Abstract

We show that large-$N$ ${\varphi }^4$ theory is not trivial if one accepts the presence of a tachyon with a truly huge mass, and that it allows exact calculation. We use it to illustrate how to calculate the exact resummed pressure at finite temperature and verify that it is infrared and ultraviolet finite even in the zero-mass case. In 3 dimensions a residual effect of the resummed infrared divergences is that at low temperature or strong coupling the leading term in the interaction pressure becomes independent of the coupling and is 4/5 of the free-field pressure. In 4 dimensions the pressure is well-defined provided that the temperature is below the tachyon mass. We examine how rapidly this expansion converges and use our analysis to suggest how one might reorganise perturbation theory to improve the calculation of the pressure for the QCD plasma.

18 pages plain tex, with 8 figures embedded with epsf. Equation (2.15) has been corrected and the consequent changes made to the figures. A further analytic result has been added to the 3-dimensional calculation

References in corpus (6)

• Screened Perturbation Theory
• Thermal Effective Potential of the O(N) Linear sigma Model
• Perturbative Finite-Temperature Results and Pad'e Approximants
• Nonperturbative Higgs propagator: NLO correction in the 1/N expansion
• Non-perturbative Evaluation of the Effective Potential of $\lambda {\varphi }^4$ Theory at Finite Temperature under the Super-Daisy Approximation
• Introduction to Thermal Field Theory: From First Principles to Applications

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