https://doi.org/10.1140/epjc/s10052-020-7646-y
Regular Article - Theoretical Physics
Vacuum instability in a constant inhomogeneous electric field: a new example of exact nonperturbative calculations
1
Department of Physics, College of Physical Sciences and Technology, Hebei University, Wusidong Road 180, 071002, Baoding, China
2
Department of Physics, Tomsk State University, Lenin Prospekt 36, 634050, Tomsk, Russia
3
Department of General and Experimental Physics, Herzen State Pedagogical University of Russia, Moyka embankment 48, 191186, St. Petersburg, Russia
4
P. N. Lebedev Physical Institute, 53 Leninskiy prospekt, 119991, Moscow, Russia
5
Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, CEP 05508-090, São Paulo, S.P., Brazil
Received:
5
December
2019
Accepted:
10
January
2020
Published online:
4
February
2020
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 
(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.
© The Author(s) 2020
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