Schwinger pair production: Explicit Localization of the world-line instanton

TL;DR

This paper provides a straightforward proof that the world-line path integral's imaginary part, calculating Schwinger pair production rates in a constant electric field, matches the semiclassical WKB approximation exactly.

Contribution

It offers a simple, rigorous proof linking the world-line path integral to the semiclassical WKB limit for Schwinger pair production.

Findings

The imaginary part of the world-line path integral equals the semiclassical WKB result.

The proof simplifies understanding of pair production rate calculations.

The approach clarifies the connection between path integrals and semiclassical methods.

Abstract

We present a simple proof that the imaginary part of the world-line path integral which computes the rate of Schwinger pair production of charged particles in a constant electric field, is given exactly by the semiclassical WKB limit.