On the need for soft dressing

TL;DR

The paper addresses infrared divergences in QED and perturbative quantum gravity by comparing inclusive, Fock-space calculations with Faddeev-Kulish–type dressed states. For discrete and continuous incoming superpositions, the inclusive formalism destroys interference or even negates scattering in the hard sector, while the dressed formalism preserves interference and yields IR-finite S-matrix elements $\\mathbb{S}_{\\beta\\alpha} = \\langle \\beta| W_\\beta^\\dagger S W_\\alpha |\\alpha\\rangle$, leading to cross-sections that include interference terms. The authors interpret these results through the lens of asymptotic symmetries and selection sectors, arguing that physical superpositions must lie within the same sector and that dressed states provide a more consistent description of scattering. They also discuss the implications for black hole information and the structure of the IR-complete Hilbert space, suggesting that the von Neumann space with soft radiation clouds underpins observable quantum interference. Overall, the work advocates dressing as the physically correct framework for scattering involving incoming superpositions and highlights testable distinctions between formalisms.

Abstract

In order to deal with IR divergences arising in QED or perturbative quantum gravity scattering processes, one can either calculate inclusive quantities or use dressed asymptotic states. We consider incoming superpositions of momentum eigenstates and show that in calculations of cross-sections these two approaches yield different answers: in the inclusive formalism no interference occurs for incoming finite superpositions and wavepackets do not scatter at all, while the dressed formalism yields the expected interference terms. This suggests that rather than Fock space states, one should use Faddeev-Kulish-type dressed states to correctly describe physical processes involving incoming superpositions. We interpret this in terms of selection rules due to large U(1) gauge symmetries and BMS supertranslations.

Figures (1)

• Figure 1: (a) A plane wave goes through a single slit and emerges as a localized wavepacket. The scattering of the incoming wavepacket results in the production of Bremsstrahlung. (b) We can also define some Cauchy slice $\Sigma$ and create the state by an appropriate initial condition. (c) Evolving this state backwards in time while forgetting about the slit results in an incoming localized particle which is accompanied by a radiation shockwave.