Is the photon paramagnetic?

TL;DR

This paper investigates the tiny paramagnetic magnetic moment of photons caused by their interaction with external magnetic fields, providing explicit formulas and analyzing behavior near pair creation thresholds.

Contribution

It introduces explicit expressions for the photon magnetic moment in different energy regimes and discusses mode dependence and behavior near pair creation thresholds.

Findings

Photon exhibits a positive magnetic moment in vacuum under magnetic fields.

Magnetic moment varies for different polarization modes.

Maximum magnetic moment occurs near the pair creation threshold.

Abstract

A photon exhibits a tiny anomalous magnetic moment $\mu_{\gamma}$ due to its interaction with an external constant magnetic field in vacuum through the virtual electron-positron background. It is paramagnetic ($\mu_{\gamma}>0$) in the whole region of transparency, i.e. below the first threshold energy for pair creation and has a maximum near this threshold. The photon magnetic moment is different for eigenmodes polarized along and perpendicular to the magnetic field. Explicit expressions are given for $\mu_{\gamma}$ for the cases of photon energies smaller and closer to the first pair creation threshold. The region beyond the first threshold is briefly discussed.