Time evolution of the QED vacuum in a uniform electric Field: Complete analytic solution by spinorial decomposition

TL;DR

This paper provides an exact analytical solution for the time evolution of pair production in the QED vacuum under a uniform electric field using spinorial decomposition, revealing nonperturbative quantum tunneling effects.

Contribution

It introduces a complete analytic solution to the Dirac-Heisenberg-Wigner function evolution via spinorial decomposition, simplifying the analysis of pair production in a uniform electric field.

Findings

Explicit solutions show nonanalytic behavior of pair production.

Analytical approach simplifies the study of time evolution in QED vacuum.

Solution demonstrates nonperturbative quantum tunneling effects.

Abstract

Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a time-independent, uniform electric field. The mathematical tool used here to describe the pair production is the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825 (1991)]. The initial value problem for this function is solved by decomposing the solution into a product of spinors. The equations for spinors are much simpler and are solved analytically. These calculations are nonperturbative since pair production is due to quantum-mechanical tunneling and the explicit solutions clearly exhibit their nonanalytic behavior.