Radiative corrections in quantum electrodynamics with intense field and their analytical properties

Abstract

Diagonalization and general properties of the mass and polarization operators and Greens functions of an electron and a photon in an intense crossed field are considered exactly in the external and radiation fields. Their explicit expressions are obtained in the e 2-approximation in the radiation field, and exactly in the external field. On the mass shell they determine the elastic scattering amplitudes and other physical quantities, for example, the dependence of the anomalous magnetic moment of the electron on the field and particle momentum. Due to instability of the electron and photon in the field, the analytic properties of the mass and polarization operators differ from those in vaccum; they become entire transcendental functions of the momentum square and depend nontrivially on the dynamic variable which is proportional to the particle momentum and to the field and in which these operators have an essential singularity and branching at zero. The Greens functions in the complex momentum square plane, besides the one-particle pole, have an infinite number of poles instead of the branching and cut which correspond to the spectrum of two-particle states. All the poles depend on the dynamic variable and have imaginary parts of the appropriate sign which provide correct causal properties. Different branches in the dynamic variable form retarded and advanced functions. The fourth-order radiative corrections to the elastic scattering amplitude of an electron, due to vacuum polarization, are obtained and the limits on perturbation theory are found.