Spectral-integral representation of the photon polarization operator in   a constant uniform magnetic field
  The polarization operator in a constant and homogeneous magnetic field of arbitrary strength is investigated on mass shell. The calculations are carried out at all photon energies higher the pair creation threshold as well as lower this threshold. The general formula for the effective mass of the photon with given polarization has been obtained being useful for an analysis of the problem under consideration as well as at a numerical work. Approximate expressions for strong or weak fields, compared with the critical field, have been found. Depending on the ratio of these fields we consider the pure quantum region of photon energy, where particles are created on lower Landau levels or created not at all. Also the energy region of large level numbers is considered where the quasiclassical approximation is valid. 
V.M. Katkov
hep-th