Polarization rotation for light propagating non-parallel to a magnetic field in QED vacuum and in a dilute electron gas

TL;DR

This paper investigates polarization rotation effects for light in magnetic fields within quantum electrodynamics, comparing vacuum and dilute electron gas scenarios, and relates findings to experimental and astrophysical contexts.

Contribution

It introduces a detailed calculation of polarization rotation in QED vacuum and dilute electron gas, highlighting differences with the Faraday effect and connecting results to PVLAS experiments.

Findings

Polarization vector describes an ellipse with periodically varying axes.

Rotation angles compatible with PVLAS experimental limits.

Results have implications for astrophysical phenomena.

Abstract

The rotation of the polarization vector for light propagating perpendicular to an external constant external magnetic field $B$, is calculated in quantum vacuum, where it leads to different photon eigenmodes of the magnetized photon self-energy tensor for polarizations along and orthogonal to $B$ (Cotton-Mouton effect in QED vacuum). Its analogies and differences with Faraday effect are discussed and both phenomena are calculated for a relativistic electron gas at low densities, by starting from the low energy limit of the photon self-energy eigenvalues in presence of $B$. In the Cotton-Mouton case the polarization vector describes an ellipse whose axes vary periodically from zero to a maximum value. By assuming an effective electron density of order $10^3$ cm$^{-3}$ the quantum relativistic eigenvalues lead to a rotation of the polarization plane compatible with some of the limit values reported by PVLAS experiments. Other consequences, which are interesting for astrophysics, are also discussed.