BMS Supertranslation Symmetry Implies Faddeev-Kulish Amplitudes

TL;DR

This paper demonstrates that Faddeev-Kulish states naturally emerge from BMS supertranslation symmetries in gravity, ensuring infrared finite scattering amplitudes and revealing the symmetry-based origin of these states.

Contribution

It explicitly links BMS supertranslation symmetry to Faddeev-Kulish states, showing their equivalence in constructing infrared-finite scattering amplitudes in gravity.

Findings

Charge-conserving amplitudes match Faddeev-Kulish constructions.

Faddeev-Kulish clouds can be transferred between in and out states without losing finiteness.

Soft boson effects cause decoherence of hard particle momentum states.

Abstract

We show explicitly that, among the scattering amplitudes constructed from eigenstates of the BMS supertranslation charge, the ones that conserve this charge, are equal to those constructed from Faddeev-Kulish states. Thus, Faddeev-Kulish states naturally arise as a consequence of the asymptotic symmetries of perturbative gravity and all charge conserving amplitudes are infrared finite. In the process we show an important feature of the Faddeev-Kulish clouds dressing the external hard particles: these clouds can be moved from the incoming states to the outgoing ones, and vice-versa, without changing the infrared finiteness properties of S matrix elements. We also apply our discussion to the problem of the decoherence of momentum configurations of hard particles due to soft boson effects.