Comments on QED with background electric fields

TL;DR

This paper demonstrates that in QED with background electric fields capable of pair production, the usual IR divergence cancellation seen in standard QED does not occur, indicating a fundamental difference in divergence behavior.

Contribution

It shows that IR divergence cancellation fails in QED with background electric fields, contrasting with the factorizable IR divergences in standard interacting theories.

Findings

IR divergences do not factorize in QED with background electric fields

Total cancellation of IR divergences does not occur in this setting

Background electric fields alter the divergence structure of QED

Abstract

It is well known that there is a total cancellation of the \emph{factorizable} IR divergences in unitary interacting field theories, such as QED and quantum gravity. In this note we show that such a cancellation does not happen in QED with background electric fields which can produce pairs. There is no factorization of the IR divergences.