Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production

TL;DR

This paper explores complex worldline instantons in vacuum pair production, revealing how they incorporate quantum interference effects and dominate the semiclassical evaluation of pair production rates, with strong agreement to other methods.

Contribution

It introduces the concept of complex instantons in vacuum pair production and demonstrates their role in quantum interference within a semiclassical framework.

Findings

Complex instantons are essential in describing pair production.

The method shows excellent agreement with alternative approaches.

Quantum interference effects are captured by phase factors in complex trajectories.

Abstract

We describe in detail a physical situation in which instantons are necessarily complex, not just Wick rotations of classical solutions to Euclidean spacetime. These complex instantons arise in the semiclassical evaluation of vacuum pair production rates, based on Feynman's worldline path integral formulation. Even though the path integral is a sum over all real closed trajectories in spacetime, the semiclassical description of non-perturbative pair production is dominated by closed classical trajectories that are generically complex. These closed trajectories contain segments associated with nonperturbative instanton suppression factors as well as segments producing phase factors that incorporate quantum interference effects. For a class of time-dependent electric fields we implement this procedure and demonstrate excellent quantitative agreement with alternative methods.