Nonlinear electrodynamics in a superstrong magnetic field

Using a Feynman technique in a two-dimensional space we have calculated an electron propagator and a photon polarization tensor in a superstrong magnetic field $\text{B ? B}{}_{\mathrm{<mtext>0</mtext>}}\text{=}\text{m}{}^{\mathrm{<mtext>2</mtext>}}\text{e}\text{=}\text{4.41 × 10}{}^{13}$ G. Some applications are briefly discussed.