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.