Tunnelling amplitudes and Hawking radiation from worldline QFT

TL;DR

This paper uses the worldline quantum field theory approach to compare Hawking radiation and Schwinger pair creation, revealing how tunnelling amplitudes relate to complex saddle points in different backgrounds.

Contribution

It introduces a unified worldline framework to analyze tunnelling processes in gravity and QED, connecting Hawking radiation with Schwinger pair creation.

Findings

Constructed solutions using worldline approach for both effects.

Identified complex saddle points as key to tunnelling amplitudes.

Unified perspective on quantum tunnelling in gravitational and electromagnetic fields.

Abstract

We compare Hawking radiation in a collapse background with Schwinger pair creation in an electric field. The comparison is driven by the presence of an analogue horizon in the Schwinger case, which causally divides spacetime for classical particles, but through which quantum fields can tunnel. Amplitudes for tunnelling processes are encoded in the asymptotic behaviour of solutions to the appropriate background-coupled wave equation. We construct these solutions, in both gravity and QED, using the worldline approach, where tunnelling and particle creation manifest as complex saddle points of a real-time path integral. For the Schwinger effect, these saddles correspond to complex worldlines, while for Hawking radiation, the corresponding worldlines are real, but appear complex when extended beyond a certain coordinate patch.