Derivative expansion of the heat kernel at finite temperature

Details Derivative expansion of the heat kernel at finite temperature Derivative expansion of the heat kernel at finite temperature

2011-10-28

arxiv.org/abs/1110.6300v2

Phys.Rev.D85: 045019, 2012

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1103/PhysRevD.85.045019

The method of covariant symbols of Pletnev and Banin is extended to space-times with topology $\R^n\times S^1\times ... \times S^1$. 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.

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