Nonlinear interaction between electromagnetic fields at high temperature

TL;DR

This paper investigates the high-temperature behavior of the nonlinear electromagnetic interaction derived from the electron-positron loop, revealing a finite limit at infinite temperature and exploring related effects in 2D QED.

Contribution

It provides the first analysis of the high-temperature limit of the nonlinear electromagnetic effective action from the electron-positron loop.

Findings

Finite, nonzero limit of the effective action as temperature approaches infinity.

Explicit calculation of the limit in nonrelativistic static and long-wavelength regimes.

Discussion of similar effects in two-dimensional QED.

Abstract

The electron-positron `box' diagram produces an effective action which is fourth order in the electromagnetic field. We examine the behaviour of this effective action at high-temperature (in analytically continued imaginary-time thermal perturbation theory). We argue that there is a finite, nonzero limit as $T\rightarrow \infty$ (where $T$ is the temperature). We calculate this limit in the nonrelativistic static case, and in the long-wavelength limit. We also briefly discuss the self-energy in 2-dimensional QED, which is similar in some respects.