Schwinger Pair Production via Instantons in Strong Electric Fields

TL;DR

This paper links instanton solutions in quantum tunneling to pair production rates in strong electric fields, providing a unified interpretation for boson and fermion pair creation, including in inhomogeneous fields.

Contribution

It introduces an instanton-based framework to calculate and interpret pair production rates in strong electric fields, extending to inhomogeneous cases and fermions.

Findings

Instanton interpretation reproduces known pair production rates for uniform fields.

The method applies to inhomogeneous electric fields, providing new computational tools.

Bosons and fermions cannot be produced by static magnetic fields alone.

Abstract

In the space-dependent gauge, each mode of the Klein-Gordon equation in a strong electric field takes the form of a time-independent Schr\"{o}dinger equation with a potential barrier. We propose that the single- and multi-instantons of quantum tunneling may be related with the single- and multi-pair production of bosons and the relative probability for the no-pair production is determined by the total tunneling probability via instantons. In the case of a uniform electric field, the instanton interpretation recovers exactly the well-known pair production rate for bosons and when the Pauli blocking is taken into account, it gives the correct fermion production rate. The instanton is used to calculate the pair production rate even in an inhomogeneous electric field. Furthermore, the instanton interpretation confirms the fact that bosons and fermions can not be produced by a static magnetic field only.