Schwinger Pair Production in Electric and Magnetic Fields

TL;DR

This paper derives formulas for Schwinger pair production rates in combined electric and magnetic fields, accounting for Landau levels and boundary effects, using the instanton method in quantum electrodynamics.

Contribution

It provides a comprehensive derivation of pair-production rates in static fields with magnetic components, including boundary effects, extending previous results.

Findings

Derived explicit formulas for pair-production rates in combined fields.

Calculated rates for finite electric fields with magnetic fields present.

Identified boundary effects influencing pair production.

Abstract

Charged particles in static electric and magnetic fields have Landau levels and tunneling states from the vacuum. Using the instanton method of Phys. Rev. D 65, 105002 (2002), we obtain the formulae for the pair-production rate in spinor and scalar QED, which sum over all Landau levels and recover exactly the well-known results. The pair-production rates are calculated for an electric field of finite extent, with a constant magnetic field also present, and are shown to have boundary effects.