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.
Highlights
In the framework of QED with a strong background, we study particle creation by a time-dependent inverse square electric field
In the present article we study the vacuum instability in an inverse square electric field; see its exact definition
This behavior is characteristic for an effective mean electric field in graphene, which is a deformation of the initial constant electric field by backreaction due to the vacuum instability; see Ref. [32]
Summary
In the present article we study the vacuum instability in an inverse square electric field (an electric field that is inversely proportional to time squared); see its exact definition . This behavior is characteristic for an effective mean electric field in graphene, which is a deformation of the initial constant electric field by backreaction due to the vacuum instability; see Ref. 2 we present, for the first time, exact solutions of the Dirac and Klein–Gordon equations with the inverse square electric field in the Minkowski space-time.
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