The Polyakov loop and the heat kernel expansion at finite temperature

TL;DR

This paper computes the lower order terms of the heat kernel expansion at finite temperature in gauge theories, emphasizing the role of the Polyakov loop and ensuring gauge invariance in the imaginary time formalism.

Contribution

It provides a detailed calculation of heat kernel terms at finite temperature, highlighting the significance of the Polyakov loop in gauge invariance and non-stationary fields.

Findings

Heat kernel expansion terms are computed at finite temperature.

Polyakov loop is fundamental in the analysis.

Results are consistent with gauge invariance.

Abstract

The lower order terms of the heat kernel expansion at coincident points are computed in the context of finite temperature quantum field theory for flat space-time and in the presence of general gauge and scalar fields which may be non Abelian and non stationary. The computation is carried out in the imaginary time formalism and the result is fully consistent with invariance under topologically large and small gauge transformations. The Polyakov loop is shown to play a fundamental role.