A comment on generalized Schwinger effect

TL;DR

This paper examines how the rate of particle pair production in a time-dependent electric field depends on the coupling constant, revealing conditions under which this dependence is analytic or non-analytic.

Contribution

It provides a detailed analysis of the coupling constant dependence in particle production for different classes of time-dependent electric fields.

Findings

Non-analytic dependence for certain slowly varying fields.

Analytic dependence for rapidly varying fields.

Dependence varies with the asymptotic behavior of the electric field.

Abstract

A spatially homogeneous, time-dependent, electric field can produce charged particle pairs from the vacuum. When the electric field is constant, the mean number of pairs which are produced depends on the electric field and the coupling constant in a non-analytic manner, showing that this result cannot be obtained from the standard perturbation theory of quantum electrodynamics. When the electric field varies with time and vanishes asymptotically, the result may depend on the coupling constant either analytically or non-analytically. We investigate the nature of this dependence in detail. We show that the dependence of particle production on coupling constant is non-analytic for a class of time-dependent electric fields which vanish asymptotically when a specific condition is satisfied. We also demonstrate that for another class of electric fields, which vary rapidly, the dependence of particle production on coupling constant is analytic.