Pair production from residues of complex worldline instantons

TL;DR

This paper investigates nonperturbative electron-positron pair production in electric fields with lightlike inhomogeneities using complex worldline instantons, revealing a residue-based integral approach and invariance under complex reparameterisations.

Contribution

It introduces a novel complex contour integral framework for pair production via worldline instantons, connecting the process to Cauchy's residue theorem and complex reparameterisation invariance.

Findings

Pair production probability expressed as a complex contour integral.

Instanton contributions correspond to residues from poles.

Invariance under complex reparameterisations demonstrated.

Abstract

We study nonperturbative pair production in electric fields with lightlike inhomogeneities, using complex worldline instantons. We show that the instanton contribution to the pair production probability is a complex contour integral over the instanton itself, and that pair production in the considered fields can be recast in terms of Cauchy's residue theorem. The instantons contribute residues from the poles they circulate (i.e. give local contributions), and the invariance of complex integrals under contour deformation manifests in the instanton contributions as invariance under a set of generalised, complex, reparameterisations.