Infrared physics of QED and gravity from representation theory

TL;DR

This paper explores how the unitary irreducible representations of asymptotic symmetry groups in QED and gravity encode universal infrared features, aiming to define an infrared-finite S-matrix and contrasting with dressed-state methods.

Contribution

It introduces a representation-theoretic framework for understanding infrared structures in QED and gravity, proposing a new approach to infrared-finite scattering amplitudes.

Findings

UIRs encode universal infrared features

Construction of supermomentum eigenstates

Comparison with dressed-state approach

Abstract

The infrared structure of QED and gravity is known to be governed by an infinite-dimensional symmetry group which extends the Poincar\'e group to include, respectively, large $U(1)$ transformations and BMS supertranslations. We describe how the unitary irreducible representations (UIRs) of these asymptotic symmetry groups encode universal infrared features of a scattering process. Motivated by the goal of defining an infrared-finite $S$-matrix based on these UIRs, we also study supermomentum eigenstates and contrast our construction with the dressed-state approach for infrared-safe amplitudes.