Worldline instantons for the momentum spectrum of Schwinger pair production in space-time dependent fields

TL;DR

This paper develops a semiclassical worldline-instanton approach to compute the momentum spectrum of electron-positron pairs produced by space-time dependent electric fields, extending previous methods to more complex field configurations.

Contribution

It introduces a novel application of the worldline-instanton formalism combined with the LSZ reduction to analyze pair production in general space-time dependent fields.

Findings

Derived a semiclassical approximation for the pair-production spectrum.

Validated the spectrum calculation by comparing integrated results with previous instanton methods.

Extended the applicability of instanton techniques to more realistic, inhomogeneous fields.

Abstract

We show how to use the worldline-instanton formalism to calculate the momentum spectrum of the electron-positron pairs produced by an electric field that depends on both space and time. Using the LSZ reduction formula with a worldline representation for the propagator in a spacetime field, we make use of the saddle-point method to obtain a semiclassical approximation of the pair-production spectrum. In order to check the final result, we integrate the spectrum and compare with the results obtained using a previous instanton method for the imaginary part of the effective action.