Light Cone Condition for a Thermalized QED Vacuum

TL;DR

This paper derives the light cone condition for low-frequency light in a thermalized QED vacuum, calculating velocity shifts and refractive indices influenced by temperature and magnetic fields, revealing a maximum velocity shift at intermediate temperatures.

Contribution

It provides a Lorentz covariant, gauge-invariant derivation of the light cone condition in a thermalized QED vacuum, including effects of temperature and magnetic fields, and identifies a maximum velocity shift at T~m.

Findings

Velocity shifts depend on temperature and magnetic fields.

Low-temperature effects are exponentially suppressed.

Maximum velocity shift occurs at T~electron mass.

Abstract

Within the QED effective action approach, we study the propagation of low-frequency light at finite temperature. Starting from a general effective Lagrangian for slowly varying fields whose structure is solely dictated by Lorentz covariance and gauge invariance, we derive the light cone condition for light propagating in a thermalized QED vacuum. As an application, we calculate the velocity shifts, i.e., refractive indices of the vacuum, induced by thermalized fermions to one loop. We investigate various temperature domains and also include a background magnetic field. While low-temperature effects to one loop are exponentially damped by the electron mass, there exists a maximum velocity shift of $-\delta v^2_{max}=\alpha/(3\pi)$ in the intermediate-temperature domain $T\sim m$.