Series expansion of the photon self-energy in QED and the photon anomalous magnetic moment
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We start from the analytical expression of the eigenvalues $κ^{(i)}$ 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 $κ^{(i)}$. A general expression is given for the photon anomalous magnetic moment $μ_γ>0$ 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 $μ_γ>0$ are displayed in a region close to the threshold.