A simple way to take into account back reaction on pair creation

TL;DR

This paper introduces a straightforward method to incorporate back reaction effects from pair creation in scalar QED, providing a simple formula for the decay rate of a constant electric field, with potential applications to gravity backgrounds.

Contribution

A simple, systematic approach to include back reaction effects in pair creation calculations, generalizable to gravity backgrounds.

Findings

Derived a simple formula for electric field decay rate due to pair creation.

Method applicable to scalar QED and extendable to gravity backgrounds.

Provides a systematic way to account for back reaction effects.

Abstract

We propose a simple and systematic way of accounting for the back reaction on the background field due to the pair creation in the four--dimensional scalar QED. This method is straightforwardly generalizable to the gravity backgrounds. In the case of QED with the instantly switched on constant electric field background we obtain a remarkably simple formula for its decay rate.