Secularly growing loop corrections in strong electric fields

We calculate one-loop corrections to the vertexes and propagators of photons and charged particles in the strong electric field backgrounds. We use the Schwinger-Keldysh diagrammatic technique. We observe that photon's Keldysh propagator receives growing with time infrared contribution. As the result, loop corrections are not suppressed in comparison with tree-level contribution. This effect substantially changes the standard picture of the pair production. To sum up leading IR corrections from all loops we consider the infrared limit of the Dyson-Schwinger equations and reduce them to a single kinetic equation.