Kinetic theory of vacuum pair production in uniform electric fields revisited

TL;DR

This paper revisits the quantum kinetic theory of vacuum electron-positron pair production in uniform, time-dependent electric fields, correcting previous models, establishing equivalence between formalisms, and analyzing spin effects.

Contribution

It derives a corrected set of quantum kinetic equations for rotating electric fields and proves their equivalence with the Dirac-Heisenberg-Wigner formalism, including spin effects.

Findings

Corrected quantum kinetic equations for rotating fields.

Established equivalence between QKEs and DHW formalism.

Analyzed spin effects in particle distributions.

Abstract

We investigate the phenomenon of electron-positron pair production from vacuum in the presence of a uniform time-dependent electric field of arbitrary polarization. Taking into account the interaction with the external classical background in a nonperturbative manner, we quantize the electron-positron field and derive a system of ten quantum kinetic equations (QKEs) showing that the previously-used QKEs are incorrect once the external field rotates in space. We employ then the Wigner-function formalism of the field quantization and establish a direct connection between the Dirac-Heisenberg-Wigner (DHW) approach to investigating the vacuum pair-production process and the QKEs. We provide a self-contained description of the two theoretical frameworks rigorously proving their equivalence and present an exact one-to-one correspondence between the kinetic functions involved within the two techniques. Special focus is placed on the analysis of the spin effects in the final particle distributions.