Vacuum instability in a constant inhomogeneous electric field. A new example of exact nonperturbative calculations

TL;DR

This paper presents exact nonperturbative calculations of quantum processes like particle creation and vacuum instability caused by inverse-square electric fields, providing new insights into QED in inhomogeneous backgrounds.

Contribution

It introduces exact solutions for Dirac and Klein-Gordon equations in inverse-square electric fields and analyzes vacuum instability in various configurations, a novel approach in QED.

Findings

Exact solutions for particle creation in inverse-square electric fields.

Comparison of analytical and numerical results for vacuum instability.

Insights into the role of field gradients in vacuum decay processes.

Abstract

Basic quantum processes (such as particle creation, reflection, and transmission on the corresponding Klein steps) caused by inverse-square electric fields are calculated. These results represent a new example of exact nonperturbative calculations in the framework of QED. The inverse-square electric field is time-independent, inhomogeneous in the $x$-direction, and is inversely proportional to $x$ squared. We find exact solutions of the Dirac and Klein-Gordon equations with such a field and construct corresponding in- and out-states. With the help of these states and using the techniques developed in the framework of QED with $x$-electric potential steps, we calculate characteristics of the vacuum instability, such as differential and total mean numbers of particles created from the vacuum and vacuum-to-vacuum transition probabilities. We study the vacuum instability for two particular backgrounds: for fields widely stretches over the $x$-axis (small-gradient configuration) and for the fields sharply concentrates near the origin $x=0$ (sharp-gradient configuration). We compare exact results with ones calculated numerically. Finally, we consider the electric field configuration, composed by inverse-square fields and by an $x$-independent electric field between them to study the role of growing and decaying processes in the vacuum instability.