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

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.