Nonperturbative pair production in interpolating fields

TL;DR

This paper investigates how different types of inhomogeneities in strong electromagnetic fields affect nonperturbative pair production, providing a unified framework using interpolating coordinates and analyzing the role of branch cuts and poles in the effective action.

Contribution

It introduces a unifying approach to analyze pair production in various inhomogeneous fields using complex worldline instantons and interpolating coordinates.

Findings

Spacelike inhomogeneities relate to critical points via branch cut lengths.

Lightlike inhomogeneities simplify instanton calculations by contracting cuts to poles.

Effective action behavior varies with field dependence and number of components.

Abstract

We compare the effects of timelike, lightlike and spacelike one-dimensional inhomogeneities on the probability of nonperturbative pair production in strong fields. Using interpolating coordinates we give a unifying picture in which the effect of the inhomogeneity is encoded in branch cuts and poles circulated by complex worldline instantons. For spacelike inhomogeneities the length of the cut is related to the existence of critical points, while for lightlike inhomogeneities the cut contracts to a pole and the instantons become contractable to points, leading to simplifications particular to the lightlike case. We calculate the effective action in fields with up to three nonzero components, and investigate its behaviour under changes in field dependence.