World-line instantons and the Schwinger effect as a WKB exact path integral

TL;DR

This paper demonstrates that the WKB approximation for the world line path integral in a constant electric field is exact, with all higher-order corrections vanishing, thus precisely reproducing the Schwinger pair production formula.

Contribution

It proves the exactness of the WKB approximation for the world line path integral in a constant electric field, confirming the Schwinger formula without additional corrections.

Findings

WKB approximation is exact for the world line path integral in a constant electric field.

All fluctuation corrections beyond leading order vanish.

The Schwinger pair production formula is exactly reproduced by the semiclassical expansion.

Abstract

A detailed study of the semiclassical expansion of the world line path integral for a charged relativistic particle in a constant external electric field is presented. We show that the Schwinger formula for charged particle pair production is reproduced exactly by the semiclassical expansion around classical instanton solutions when the leading order of fluctuations is taken into account. We prove that all corrections to this leading approximation vanish and that the WKB approximation to the world line path integral is exact.