Finite temperature nonlocal effective action for quantum fields in curved space

TL;DR

This paper derives the finite temperature nonlocal effective action and free energy for various quantum fields in curved spacetime, providing infrared divergence-free expressions and spectral representations for high temperature expansions.

Contribution

It presents the first derivation of the finite temperature nonlocal effective action for scalar and spinor fields in curved spacetime, including selfinteractions and conformal cases, up to second order.

Findings

Effective action free of infrared divergences.

Spectral representations for high temperature expansions.

Explicit expressions for scalar and spinor fields at finite temperature.

Abstract

Massless and massive scalar fields and massless spinor fields are considered at arbitrary temperatures in four dimensional ultrastatic curved spacetime. Scalar models under consideration can be either conformal or nonconformal and include selfinteraction. The one-loop nonlocal effective action at finite temperature and free energy for these quantum fields are found up to the second order in background field strengths using the covariant perturbation theory. The resulting expressions are free of infrared divergences. Spectral representations for nonlocal terms of high temperature expansions are obtained.