One-loop finite temperature effective action of QED in the worldline approach

TL;DR

This paper derives the one-loop finite temperature effective action of QED in external electromagnetic fields using the worldline approach, providing a general structure and specific two-derivative results for static magnetic backgrounds.

Contribution

It introduces a novel application of the worldline method to finite temperature QED, deriving the effective action in inhomogeneous and static magnetic fields.

Findings

General structure of temperature-dependent effective action established

Two-derivative effective action derived for static magnetic backgrounds

Applicable to inhomogeneous electromagnetic fields at finite temperature

Abstract

The one-loop finite temperature effective potential of QED in an external electromagnetic field is obtained using the worldline method. The general structure of the temperature dependent part of the effective action in an arbitrary external inhomogeneous magnetic field is established. The two-derivative effective action of spinor and scalar QED in a static magnetic background at $T\neq 0$ is derived.