Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering

TL;DR

This paper develops a novel worldline instanton formalism on the amplitude level, enabling detailed analysis of nonlinear Breit-Wheeler pair production and Compton scattering, extending previous probability-based approaches.

Contribution

It introduces a new open instanton line approach on the amplitude level for studying pair production and scattering processes.

Findings

Formalism for amplitude-level instantons established

Application to photon-stimulated pair production demonstrated

Extension to nonlinear Compton scattering achieved

Abstract

Worldline instantons have previously been used to study the probability of Schwinger pair production (both the exponential and pre-exponential parts) and photon-stimulated pair production (the exponential part). Previous studies obtained the pair-production probability on the probability level by using unitarity, i.e. the imaginary part of the effective action for Schwinger pair production or the imaginary part of the polarization tensor for photon-stimulated pair production. The corresponding instantons are closed loops in the complex plane. Here we show how to use instantons on the amplitude level, which means open instanton lines with start and end points representing fermions at asymptotic times. The amplitude is amputated with LSZ using, in general, field-dependent asymptotic states. We show how to use this formalism for photon-stimulated/Breit-Wheeler pair production and nonlinear Compton scattering.