Thermal effective Lagrangian of generalized electrodynamics in static gravitational fields

TL;DR

This paper calculates the thermal effective Lagrangian for generalized electrodynamics in static gravitational fields at high temperature, revealing symmetries and the Tolman local temperature using Matsubara formalism.

Contribution

It provides a closed-form expression for the thermal effective Lagrangian at one- and two-loop order in arbitrary dimensions, exploring the equivalence of static hard thermal loops.

Findings

Derived the effective Lagrangian in arbitrary dimensions.

Confirmed the equivalence of static hard thermal loops with zero external energy-momentum.

Discussed the role of the Tolman local temperature.

Abstract

In this paper we compute the effective Lagrangian of static gravitational fields interacting with thermal fields of generalized electrodynamics at high temperature. We employ the usual Matsubara imaginary-time formalism to obtain a closed form expression to the thermal effective Lagrangian at one-loop and two-loop order, in an arbitrary $\omega$-dimensional spacetime, in which the equivalence between the static hard thermal loops and those with zero external energy-momentum is widely explored. Afterwards, the symmetries of the resulting expressions are discussed as well as the presence of the Tolman \emph{local} temperature.