Radiative corrections to the electron mass operator in the two-dimensional approximation of quantum electrodynamics

A study is made into the asymptotic behavior of the diagrams that contribute in fourth order to the mass operator $M$ in a strong magnetic field $B$ in the formal limit $B\to\infty$. The principal term of $M$ increases in proportion to the first power of the field, and comparison with the contribution from the second-order diagrams gives an upper bound on the strength of the field of the form $(\alpha\xi/\ln^2\xi)\sim 1$, where $\xi=B/B_0$, $B_0=m^2/e=4.41\cdot 10^{13}$ G. In stronger fields, the perturbation series diverges.