Construction of an asymptotic S matrix for perturbative quantum gravity

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.Comment: 34 pages, 8 figure

Semiclassical Virasoro symmetry of the quantum gravity S $$ \mathcal{S} $$ -matrix

“…However in [17], the factor S (1) in (1.1) relating the 5 and 4 point amplitude was found to remain uncorrected at one loop in a scheme with the soft limit taken prior to removing the IR cutoff. 3 In the recent work [20,21] (see also [22]) it was shown that a properly defined S-matrix utilizing the gravity version of the Kulish-Faddeev construction [23] is free of all IR divergences. This may be the proper context for the discussion, as it is hard to have a symmetry of an S-matrix without an S-matrix!…”

BMS supertranslation symmetry implies Faddeev-Kulish amplitudes

“…is the anti-Hermitian operator appearing in the construction of Faddeev-Kulish state [4] with φ = 1. In contrast to M and M c , the IR-finite Faddeev-Kulish amplitude M FK is given by…”

“…These states can be interpreted as Fock states dressed by an infinite number of soft bosons, which are commonly referred to as the boson clouds. It has been shown that using a set of such states as basis yields well-defined, infrared finite S-matrix elements [3,4].…”

Asymptotic dynamics in perturbative quantum gravity and BMS supertranslations

“…The standard Dyson S-matrix between these asymptotic states is then free of infrared singularities. This Faddeev-Kulish method was extended to perturbative quantum gravity in [4]. It should be noted that the Faddeev-Kulish construction is valid in QED only for massive charged particles.…”