Euler-Heisenberg waves propagating in a magnetic background

TL;DR

This paper derives solutions for electromagnetic wave propagation in intense uniform magnetic or electric backgrounds using the effective metric approach, revealing birefringence, phase velocity modifications, and effects of background motion.

Contribution

It provides a detailed analysis of wave behavior in strong fields, including the impact of background motion, which is a novel extension of Euler-Heisenberg theory applications.

Findings

Birefringence occurs in magnetic backgrounds affecting wave polarization.

Phase velocities decrease significantly in strong magnetic fields.

Background motion influences wave propagation speed and direction.

Abstract

We derive the Euler-Heisenberg solutions that describe electromagnetic waves propagating through very intense uniform magnetic or electric background, with the effective metric approach. We first explore the case of a magnetic background: as a result of the interaction between the wave and the background there is birefringence and a longitudinal electric field component arises. The two phase velocities depend on the intensity of the external magnetic field and on the polarization of the wave; phase velocities can be slowed down up to the order of hundred thousandths for fields $B/B_{\rm cr} << 1$. The analogous study is done when the wave propagates through a uniform electric field. We then consider the situation when the background is in movement by means of a Lorentz boost, modeling then a magnetized flowing medium. We determined how this motion affects the speed of propagation of the electromagnetic wave, in this case the phase velocities depend on both the magnetic background and the direction and velocity of the boost.