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arXiv · 2603.07010

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

Sree Ram Valluri·Farrukh Chishtie·Wieslaw J. Mielniczuk
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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.

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Sree Ram Valluri, Farrukh Chishtie, Wieslaw J. Mielniczuk. 2026-03-07. Vacuum Birefringence, Ellipticity, and the Anomalous Magnetic Moment of a Photon. https://arxiv.org/abs/2603.07010

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