Secularly growing loop corrections in strong electric fields

TL;DR

This paper demonstrates that in strong electric fields, one-loop quantum corrections grow over time, significantly altering the traditional understanding of pair production by summing leading infrared effects into a kinetic equation.

Contribution

It introduces a method to sum leading infrared loop corrections in strong electric fields using Dyson--Schwinger equations, revealing non-suppressed loop effects.

Findings

Photon's Keldysh propagator exhibits infrared growth over time.

Loop corrections become comparable to tree-level contributions.

Standard pair production picture is substantially modified.

Abstract

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.