Field asymptotic behavior of a polarization operator

In the framework of the previously developed two-dimensional approximation of quantum electrodynamics the field asymptotic behavior of the photon polarization operator in a superstrong magnetic field is analyzed. It is shown that in the region $10^3\lesssim(B/B_0)\lesssim10^4$, $B_0=m^2/e$, transition to $a$ superstrong field in the individual orders of perturbation theory with subsequent summation over leads to a nonsingular expression for the photon propagator, i.e. , there is no “zero-charge” problem.