Vacuum Birefringence, Ellipticity, and the Anomalous Magnetic Moment of a Photon

TL;DR

This paper investigates photon behavior in strong magnetic fields near the Schwinger critical field, revealing how the photon’s anomalous magnetic moment and vacuum birefringence relate to measurable polarization effects, with implications for experimental detection.

Contribution

It introduces new theoretical connections between photon magnetic moments, vacuum birefringence, and polarization observables, supported by numerical verification and relevant to recent experimental findings.

Findings

Photon's Hamiltonian is convex in magnetic field B.

Photon's anomalous magnetic moment increases with B, reaching 8/3 times its value at B=0.5 B_cr.

Predictions for ellipticity and polarization degree for future experiments.

Abstract

We study photon propagation in a strong magnetic field $B\sim B_{\rm{cr}}$, where $B_{\rm cr}= \frac{m^2}{e} \simeq 4.4 \times 10^{13}$ Gauss is the Schwinger critical field. We show that the expected value of the Hamiltonian of a quantized photon for a perpendicular mode is a convex function of the magnetic field $B$. We find that the anomalous magnetic moment of a photon in the one-loop approximation is a non-decreasing function of the magnetic field $B$ in the range $0\leq B \leq 30 \, B_{\rm cr}$. We find that the anomalous magnetic moment $\mu_\gamma$ of a photon for $B=30\, B_{\rm cr}$ is $\sim 8/3$ of the anomalous magnetic moment of a photon for $B = 1/2 ~ B_{\rm cr}$. We establish new connections between $\mu_\gamma$, vacuum birefringence, and directly measurable polarization observables. Based on recent experimental observations -- including the ATLAS detection of light-by-light scattering at $8.2\sigma$ significance, IXPE X-ray polarimetry of magnetars revealing polarization degrees up to 80\%, and continuing PVLAS measurements approaching QED sensitivity -- we provide predictions for ellipticity and polarization degree as important observables for future experiments. Numerical verification of our analytical results confirms the theoretical predictions with high precision.