  In the first order of the fine structer constant, the polarization operator
of a photon is investigated in a constant and homogeneous magnetic field at
arbitrary photon energies. For weak and strong fields H, compared with the
Schwinger critical field, approximate expressions have been found. We consider
the pure quantum region of photon energy near the threshold of pair creation,
as well as the region of high energy levels where the quasiclassical
approximation is valid. The general formula has been obtained for the effective
mass of photon with given polarization. It is useful for an analysis of the
problem under consideration on the whole and at a numerical work
