Finite Temperature Nonlocal Effective Action for Scalar Fields

TL;DR

This paper derives a finite temperature, nonlocal effective action for scalar fields in curved spacetime, highlighting infrared finiteness and nonlocal terms in high temperature expansions.

Contribution

It provides the first explicit derivation of a finite temperature nonlocal effective action for scalar fields in four-dimensional curved spacetime, including infrared finite properties.

Findings

Explicit form of the one-loop nonlocal effective action at finite temperature

Infrared finiteness of the derived effective action

Identification of nonlocal terms linear in temperature in high temperature expansion

Abstract

Scalar fields at finite temperature are considered in four dimensional ultrastatic curved spacetime. One loop nonlocal effective action at finite temperature is found up to the second order in curvature expansion. This action is explicitly infrared finite. In the high temperature expansion of free energy, essentially nonlocal terms linear in temperature are derived.