The current density in quantum electrodynamics in time-dependent external potentials and the Schwinger effect

TL;DR

This paper develops a method to compute the time-dependent current density in quantum electrodynamics under external electric fields, applying it to the Sauter pulse and analyzing pair production effects.

Contribution

It introduces a new approach for calculating the time evolution of current density in QED with time-dependent external fields, correcting previous expressions and exploring quasi-particle dynamics.

Findings

Results match asymptotic pair production values at late times

Enhanced quasi-particle densities occur at intermediate times in slowly varying potentials

An alternative computational approach is proposed

Abstract

In the framework of quantum electrodynamics (QED) in external potentials, we introduce a method to compute the time-dependence of the expectation value of the current density for time-dependent homogeneous external electric fields. We apply it to the so-called Sauter pulse. For late times, our results agree with the asymptotic value due to electron-positron pair production. We correct, and compare to, a general expression derived by Serber for the linearization in the external field. Based on the properties of the current density, we argue that the appearance of enhanced quasi-particle densities at intermediate times in slowly varying sub-critical potentials is generic. Also an alternative approach, which circumvents these difficulties, is sketched.