Multidimensional Worldline Instantons

TL;DR

This paper extends the worldline instanton method to calculate vacuum pair production rates in complex, multidimensional electric fields, addressing a gap where traditional techniques like WKB are not applicable.

Contribution

It introduces a novel extension of the worldline instanton technique to handle genuinely multidimensional electric fields, enabling analysis of more realistic inhomogeneous backgrounds.

Findings

Successfully applied the method to 2D and 3D electric field configurations.

Provides a new computational approach for higher-dimensional inhomogeneous fields.

Enhances understanding of pair production in complex electromagnetic backgrounds.

Abstract

We extend the worldline instanton technique to compute the vacuum pair production rate for spatially inhomogeneous electric background fields, with the spatial inhomogeneity being genuinely two or three dimensional, both for the magnitude and direction of the electric field. Other techniques, such as WKB, have not been applied to such higher dimensional problems. Our method exploits the instanton dominance of the worldline path integral expression for the effective action.