Abstract
A new exactly solvable case in strong-field quantum electrodynamics with a time-dependent external electric field is presented. The corresponding field is given by an analytic function, which is asymmetric (in contrast to Sauter-like electric field) with respect to the time instant, where it reaches its maximum value, that is why we call it the analytic asymmetric electric field. We managed to exactly solve the Dirac equation with such a field, which made it possible to calculate characteristics of the corresponding vacuum instability nonperturbatively. We construct the so-called in- and out-solutions and with their help calculate mean differential and total numbers of created charged particles, probability of the vacuum to remain a vacuum, vacuum mean values of current density and energy-momentum tensor of the particles. We study the vacuum instability in regimes of rapidly and slowly changing analytic asymmetric electric field, and compare the obtained results with corresponding ones obtained earlier for the case of the symmetric Sauter-like electric field. We also compare exact results in the regime of slowly changing field with corresponding results obtained within the slowly varying field approximation recently proposed by two of the authors, thus demonstrating the effectiveness of such an approximation.
Highlights
Particle creation from the vacuum by strong electromagnetic and gravitational fields is a remarkable effect predicted by quantum field theory (QFT)
We study the vacuum instability in regimes of rapidly and slowly changing analytic asymmetric electric field, and compare the obtained results with corresponding ones obtained earlier for the case of the symmetric Sauter-like electric field
We present a new exactly solvable case in strong-field quantum electrodynamics (QED) with t-steps
Summary
Particle creation from the vacuum by strong electromagnetic and gravitational fields is a remarkable effect (sometimes called the Schwinger effect [1]) predicted by quantum field theory (QFT). We note that among the above exactly solvable cases only the external Sauter-like electric field is given by an analytic function, EðtÞ 1⁄4 Emaxcosh−2ðt=TSÞ; AxðtÞ 1⁄4 −TS tanh ðt=TSÞ; Emax > 0: ð3Þ. This field reaches its maximum value at t 1⁄4 tmax 1⁄4 0 and is symmetric with respect to the origin. As we will see below, it corresponds to the exactly solvable case of t-step electric field, allowing an analytical and nonperturbative study of how field asymmetry affects characteristics of the vacuum instability. Useful for us properties of confluent hypergeometric functions are given in Appendix
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