  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.
