Series expansion of the photon self-energy in QED and the photon anomalous magnetic moment

TL;DR

This paper derives a series expansion for the photon self-energy in QED under a magnetic field, providing a new expression for the photon anomalous magnetic moment and demonstrating its paramagnetic nature near pair creation thresholds.

Contribution

It introduces a power series expansion of the photon self-energy eigenvalues in a magnetic field and derives a general expression for the photon anomalous magnetic moment in the transparency region.

Findings

Photon anomalous magnetic moment is positive, indicating paramagnetism.

Numerical results near the pair creation threshold confirm the theoretical predictions.

Series expansion provides a new analytical tool for studying photon properties in magnetic fields.

Abstract

We start from the analytical expression of the eigenvalues $\kappa^{(i)}$ of the photon self-energy tensor in an external constant magnetic field $B$ calculated by Batalin Shabad in the Furry representation, and in the one-loop approximation. We expand in power series of the external field and in terms of the squared photon transverse momentum $z_2$ and (minus) transverse energy $z_1=k^2-z_2$, in terms of which are expressed $\kappa^{(i)}$. A general expression is given for the photon anomalous magnetic moment $\mu_{\gamma}>0$ in the region of transparency, below the first threshold for pair creation, and it is shown that it is positive, i.e. paramagnetic. The results of the numerical calculation for $\mu_{\gamma}>0$ are displayed in a region close to the threshold.