Derivative expansion of the heat kernel at finite temperature

Abstract

The method of covariant symbols of Pletnev and Banin is extended to space-times with topology ${\mathbb{R}}^n\times S^1\times ...\times S^1$. By means of this tool, we obtain explicit formulas for the diagonal matrix elements and the trace of the heat kernel at finite temperature to fourth order in a strict covariant derivative expansion. The role of the Polyakov loop is emphasized. Chan's formula for the effective action to one loop is similarly extended. The expressions obtained formally apply to a larger class of spaces, $h$-spaces, with an arbitrary weight function $h(p)$ in the integration over the momentum of the loop.

32 pages, no figures. Subsection on real time formalism added. To appear in Phys.Rev.D

References in corpus (5)

• Aspects of the Functional Renormalisation Group
• Derivative expansion of the heat kernel in curved space
• The method of covariant symbols in curved space-time
• The Derivative Expansion at Small Mass for the Spinor Effective Action
• Direct construction of the effective action of chiral gauge fermions in the anomalous sector

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• Scattering theory without large-distance asymptotics: scattering boundary condition