Construction of an asymptotic S matrix for perturbative quantum gravity

TL;DR

This paper develops an asymptotic S matrix for perturbative quantum gravity, demonstrating all-orders IR divergence cancellation and relating soft scattering amplitudes to gravitational Wilson lines.

Contribution

It introduces a method to construct an IR-finite S matrix in quantum gravity using asymptotic states, extending techniques from QED.

Findings

All-orders IR divergence cancellation in gravitational scattering

Explicit construction of an IR-finite S matrix for quantum gravity

Relation of soft scalar scattering amplitudes to gravitational Wilson lines

Abstract

The infrared behavior of perturbative quantum gravity is studied using the method developed for QED by Faddeev and Kulish. The operator describing the asymptotic dynamics is derived and used to construct an IR-finite S matrix and space of asymptotic states. All-orders cancellation of IR divergences is shown explicitly at the level of matrix elements for the example case of gravitational potential scattering. As a practical application of the formalism, the soft part of a scalar scattering amplitude is related to the gravitational Wilson line and computed to all orders.