Currents of created pairs in strong electric fields

TL;DR

This paper computes particle creation currents in strong electric fields within QED, revealing linear growth with pulse length, divergence issues in constant fields, and insights into the Klein paradox in 2D scenarios.

Contribution

It provides detailed calculations of currents for various initial states and backgrounds in QED, highlighting differences between vacuum, thermal, and constant fields, and analyzing the Klein paradox in 2D.

Findings

Current grows linearly with pulse length in pulse backgrounds.

In constant fields, the current is either zero or diverges linearly.

Klein paradox phenomena are observed in 2D settings.

Abstract

We calculate tree--level currents of created particles in strong background electric fields in 4D QED for various initial states. Namely, we do that in pulse background for initial vacuum and thermal states at past infinity. In both cases we find that the current grows linearly with the length of the pulse with coefficients of proportionality containing the characteristic Schwinger's factor. For the constant electric field background we calculate the current for several different initial states. We observe that in such a case the current is either zero or linearly divergent. We explain the reason for such a behaviour and compare the situation in ordinary and scalar QED. Finally, we calculate the current in two--dimensional situation in the presence of such settings when the so called Klein paradox can be observed.