The SAGEX Review on Scattering Amplitudes, Chapter 13: Post-Minkowskian expansion from Scattering Amplitudes

TL;DR

This review discusses how scattering amplitudes from quantum field theory can be applied to the post-Minkowskian expansion in general relativity, offering new insights and potential improvements in gravitational wave predictions.

Contribution

It highlights the use of relativistic quantum field theory to simplify classical gravitational calculations and explores the extraction of classical physics from quantum amplitude methods.

Findings

Quantum field theory simplifies two-body scattering calculations.

Amplitude methods can derive results valid across all energy regimes.

Insights into quantum aspects of gravity influence classical physics understanding.

Abstract

The post-Minkowskian expansion of Einstein's general theory of relativity has received much attention in recent years due to the possibility of harnessing the computational power of modern amplitude calculations in such a classical context. In this brief review, we focus on the post-Minkowskian expansion as applied to the two-body problem in general relativity without spin, and we describe how relativistic quantum field theory can be used to greatly simplify analytical calculations based on the Einstein-Hilbert action. Subtleties related to the extraction of classical physics from such quantum mechanical calculations highlight the care which must be taken when both positive and negative powers of Planck's constant are at play. In the process of obtaining classical results in both Einstein gravity and supergravity, one learns new aspects of quantum field theory that are obscured when using units in which Planck's constant is set to unity. The scattering amplitude approach provides a self-contained framework for deriving the two-body scattering valid in all regimes of energy. There is hope that the full impact of amplitude computations in this field may significantly alter the way in which gravitational wave predictions will advance in the coming years.