Effective Field Theory and Applications: Weak Field Observables from Scattering Amplitudes in Quantum Field Theory

TL;DR

This paper reviews the effective field theory approach to General Relativity, focusing on calculating weak-field scattering amplitudes up to the fourth post-Minkowskian order to test and complement classical gravity predictions.

Contribution

It presents a practical scheme for evaluating classical weak-field scattering amplitudes using quantum field theory methods up to the fourth post-Minkowskian order.

Findings

Efficient calculation of weak-field scattering amplitudes up to 4PM order.

Complementary to numerical predictions in classical gravity.

Framework for testing Einstein's theory via quantum field theory.

Abstract

In this chapter, we will review the field-theoretic treatment of General Relativity based on an effective field theory extension of the Einstein-Hilbert action. This pragmatic route to low-energy quantum effects in gravity critically underpins miscellaneous investigations of phenomenological and quantum extensions of General Relativity. We discuss how it allows quantum field theory to be a theoretical laboratory for testing Einstein's theory of gravity and demonstrate the current state of the art of an efficient and practical scheme for evaluating the classical components of perturbative weak-field scattering amplitudes until the fourth post-Minkowskian order. Such results complement numerical predictions in Einstein's theory of gravity.