Violation of vacuum stability by inverse square electric fields

TL;DR

This paper investigates the Schwinger effect in quantum electrodynamics caused by inverse square electric fields, providing exact solutions and analyzing particle creation, including asymptotic regimes and comparisons with exponential fields.

Contribution

It offers the first exact solutions for particle creation in inverse square electric fields and explores their effects on vacuum stability and pair production.

Findings

Exact in- and out-solutions for Dirac and Klein-Gordon equations are derived.

Particle creation rates are calculated and shown to align with universal estimates.

Inverse square electric fields can effectively model switching processes in electric fields.

Abstract

In the framework of QED with a strong background, we study particle creation (the Schwinger effect) by a time-dependent inverse square electric field. To this end corresponding exact in- and out-solutions of the Dirac and Klein-Gordon equations are found. We calculate the vacuum-to-vacuum probability and differential and total mean numbers of pairs created from the vacuum. For electric fields varying slowly in time, we present detailed calculations of the Schwinger effect and discuss possible asymptotic regimes. The obtained results are consistent with universal estimates of the particle creation effect by electric fields in the locally constant field approximation. Differential and total quantities corresponding to asymmetrical configurations are also discussed in detail. Finally, the inverse square electric field is used to imitate switching on and off processes. Then the case under consideration is compared with the one where an exponential electric field is used to imitate switching on and off processes.