Radiation corrections to quantum processes in an intense electromagnetic field

A derivation of an asymptotic expression for the mass correction of order α to the electron propagator in an intense electromagnetic field is presented. It is used for the calculation of radiation corrections to the electron and photon elastic scattering amplitudes in the α³ approximation. All proper diagrams contributing to the amplitudes and containing the above-mentioned correction to the propagator were considered, but not those which include vertex corrections. It is shown that the expansion parameter of the perturbation theory of quantum electrodynamics in intense fields grows not slower than αχ1/3 at least for the electron amplitude, where χ=[(eF_μνp_ν)²]1/2m³, p is a momentum of the electron, and F is the electromagnetic field tensor.