The Polyakov loop and the heat kernel expansion at finite temperature

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 spacetime 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.