Temporal Klein Model for Particle-Pair Creation

José Tito Mendonça

doi:10.3390/sym13081361

Abstract

This work considers the creation of electron-positron pairs from intense electric fields in vacuum, for arbitrary temporal field variations. These processes can be useful to study quantum vacuum effects with ultra-intense lasers. We use the quantized Dirac field to explore the temporal Klein model. This model is based on a vector potential discontinuity in time, in contrast with the traditional model based on a scalar potential discontinuity in space. We also extend the model by introducing a finite time-scale for potential variations. This allows us to study the transition from a singular electric field spike, with infinitesimal duration, to the opposite case of a static field where the Schwinger formula would apply. The present results are intrinsically non-perturbative. Explicit expressions for pair-creation as a function of the potential time-scales are derived. This work explores the spacetime symmetry associated with pair creation in vacuum: the space symmetry breaking of the old Klein paradox model, in contrast with the time symmetry breaking of the temporal Klein model.

Highlights

We have explored the temporal Klein model, associated with a sharp discontinuity of the electromagnetic vector potential
This model could be relevant to experiments using ultra-short electric field spikes in vacuum, as those created by intense laser pulses with a very high-harmonic spectral content
We have considered the quantized fermionic field described by the Dirac equation, and we have focused on the influence of a finite temporal duration of the electric field spikes

Summary

Introduction

Instead, we have a sudden change of the vector potential, where emission of photon pairs is replaced by emission of electron-positron pairs This temporal Klein (or time-refraction) configuration is interesting for the study of vacuum effects by intense laser pulses, a problem that became popular in recent years [8,9,10,11]. Explicit expressions for the pair creation probability as a function of the potential time-scales are derived This could eventually be useful for ultra-intense laser experiments using high-harmonic generation. This work explores the spacetime symmetry associated with pair creation in vacuum: the space symmetry breaking of the old Klein paradox, in contrast with the time symmetry breaking of the present temporal Klein model.

Basic Formulation

Temporal Discontinuity

Finite Time Scales

Conclusions