Discrete worldline instantons

TL;DR

This paper presents a new numerical method for calculating electron-positron pair creation rates in complex spacetime-dependent fields using worldline instantons, overcoming analytical and previous numerical limitations.

Contribution

The authors develop a general, robust numerical approach to evaluate the semiclassical worldline path integral for pair production in arbitrary multi-dimensional fields.

Findings

Successfully applied to example cases of nontrivial fields

Provides full semiclassical pair production rates

Overcomes analytical and numerical challenges in the field

Abstract

The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion, i.e. worldline instantons, is possible analytically only in special cases, and a numerical treatment is nontrivial as well. We introduce a completely general numerical approach based on an approximate evaluation of the discretized path integral that easily and robustly gives the full semiclassical pair production rate in nontrivial multi-dimensional fields, and apply it to some example cases.