A photon exhibits a tiny anomalous magnetic moment ${\mu }_{\gamma }$ due to its interaction with an external constant magnetic field in vacuum through the virtual electron-positron background. It is paramagnetic (${\mu }_{\gamma }>0$) in the whole region of transparency, i.e., below the first threshold energy for pair creation, and has a maximum near this threshold. The photon magnetic moment is different for eigenmodes polarized along and perpendicular to the magnetic field. Explicit expressions are given for ${\mu }_{\gamma }$ for the cases of photon energies smaller than and closer to the first pair creation threshold. The region beyond the first threshold is briefly discussed.

• Received 22 September 2008

DOI:https://doi.org/10.1103/PhysRevD.79.093002