A few more comments on secularly growing loop corrections in strong electric fields

TL;DR

This paper demonstrates that secular growth in loop corrections for strong electric fields is gauge independent, and it analyzes photon production and current growth, revealing violations of symmetries in QED under constant electric fields.

Contribution

It extends previous work by confirming gauge independence of secular growth and solving the kinetic equation for photon production, highlighting non-zero current growth in strong electric fields.

Findings

Secular growth of loop corrections is gauge independent.

Photon production can be summed up using the kinetic equation.

One-loop correction to the current grows with time, breaking symmetries.

Abstract

We extend the observations of our previous paper JHEP 1409, 071 (2014) [arXiv:1405.5285]. In particular, we show that the secular growth of the loop corrections to the two--point correlation functions is gauge independent: we observe the same growth in the case of the static gauge for the constant background electric field. Furthermore we solve the kinetic equation describing photon production from the background fields, which was derived in our previous paper and allows one to sum up leading secularly growing corrections from all loops. Finally, we show that in the constant electric field background the one--loop correction to the current of the produced pairs is not zero: it also grows with time and violates time translational and reversal invariance of QED on the constant electric field background.