Photon propagation in non-trivial backgrounds

TL;DR

This paper presents a unified matrix eigenvalue approach to analyze photon propagation in various non-trivial backgrounds, such as thermal baths and magnetic fields, highlighting the role of polarization vectors as eigenvectors.

Contribution

It introduces a novel unified framework casting photon propagation in complex backgrounds as a matrix eigenvalue problem, accounting for non-normal matrices and eigenvector distinctions.

Findings

Polarization vectors are right eigenvectors of the propagation matrix.

The polarization sum formula corresponds to the eigenvector completeness relation.

The method effectively applies to different non-trivial backgrounds.

Abstract

Propagation of photons (or of any spin-1 boson) is of interest in different kinds of non-trivial background, including a thermal bath, or a background magnetic field, or both. We give a unified treatment of all such cases, casting the problem as a matrix eigenvalue problem. The matrix in question is not a normal matrix, and therefore care should be given to distinguish the right eigenvectors from the left eigenvectors. The polarization vectors are shown to be right eigenvectors of this matrix, and the polarization sum formula is seen as the completeness relation of the eigenvectors. We show how this method is successfully applied to different non-trivial backgrounds.