Photon dispersion in a strong magnetic field

In an external magnetic field analytical properties are studied of the photon polarization tensor calculated as the electron-positron loop in the Furry picture. The polarization tensor is reexpressed as a sum over singular contributions coming from e⁺e^?-pair photocreation in semidiscrete Landau states. The solutions of the photon dispersion equation (i.e., the one for the poles of the photon propagator) are described. The shape of the photon dispersion curve obtained is responsible for the effect of photon deflection by a strong magnetic field. No physically reliable solutions, apart from spurions, are found for the longitudinal photon mode. An infinite number of solutions with complex space-momentum are found, with no apparnet ghosts among them. An attempt is made to interprete the former in terms of possible bound and quasibound states of electron and positron pairs.