Violation of vacuum stability by inverse square electric fields

T. C. Adorno, S. P. Gavrilov, D. M. Gitman

Published 2018-07-04Version 1

In this article, we study particle creation (Schwinger effect) and vacuum instability by a time-dependent inverse square electric field. Exact in and out solutions of the Dirac and Klein-Gordon equations are found. In the framework of the generalized Furry representation, we calculate differential mean numbers of pairs created from the vacuum, total numbers, and vacuum-vacuum transition probabilities. For electric fields varying slowly in time, we discuss all possible asymptotic regimes and present detailed calculations for these quantities. The obtained results are consistent with universal estimates for 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. The obtained results are compared with the case when the form of switching on and off is exponential.