QED effective action at finite temperature and density

TL;DR

This paper calculates the QED effective action at finite temperature and density in a magnetic field, revealing oscillations in free energy and deriving an effective coupling, with comparisons to renormalization group results.

Contribution

It provides a comprehensive calculation of the QED effective action at finite temperature and density, including an explicit free energy and an effective coupling in closed form.

Findings

Free energy exhibits de Haas-van Alphen oscillations.

Derived an effective coupling at finite temperature and density.

Compared effective coupling with renormalization group results.

Abstract

The QED effective action at finite temperature and density is calculated to all orders in an external homogeneous and time-independent magnetic field in the weak coupling limit. The free energy, obtained explicitly, exhibit the expected de\ Haas -- van\ Alphen oscillations. An effective coupling at finite temperature and density is derived in a closed form and is compared with renormalization group results.