  The polarization operator of a photon in a constant and uniform magnetic
field is studied taking into account the radiation width and shift of the
Landau levels in both weak and strong fields compared with the critical field
$H_0=4,41\cdot10^{13}$ G . A general formula is obtained for the polarization
operator of a photon in which radiation effects are taken into account. Now
diverging previously threshold terms have a finite value. The conditions are
formulated under which the energy levels completely overlap, and thereby the
most appropriate application of the semiclassical operator method to the
problem under study becomes.
