The ABCs of Amplitudes, Bogoliubov and Crossing

TL;DR

This paper explores the use of scattering amplitudes to describe gravitational radiation from dynamical black holes, connecting concepts like Bogoliubov coefficients, crossing symmetry, and causality within quantum field theory on backgrounds.

Contribution

It provides a reinterpretation of Bogoliubov coefficients as generalized amplitudes and relates crossing, analyticity, and causality to these amplitudes in curved backgrounds.

Findings

Reinterpreted Bogoliubov coefficients as generalized amplitudes

Linked crossing symmetry and causality to amplitude relations

Mapped background quantum states to flat-space QFT results

Abstract

It is now common to describe classical backgrounds involving dynamical black holes with the production of gravitational radiation using the methods of scattering amplitudes. In that light, we revisit the standard formulation of quantum field theory on a background. We discuss the interpretation of Bogoliubov coefficients as generalised amplitudes, and explain how crossing, analyticity, and causality relate the relevant set of amplitudes. When the background is itself a coherent state, we map these statements onto standard results in flat-space quantum field theory.