New Symmetries of QED

TL;DR

The paper extends the infrared structure of QED by deriving a Ward identity for an infinite-dimensional asymptotic symmetry in theories with massive charged matter, incorporating antipodal matching at spatial infinity. It constructs dressed asymptotic states, analyzes the action of large gauge transformations on these states, and decomposes the S-matrix charges into soft and hard parts, showing that the soft photon theorem for massive charges is equivalent to the corresponding Ward identity. Central to the approach are retarded/advanced asymptotics, the Lienard-Wiechert fields, and the antipodal i^0 matching which together ensure a consistent, gauge-invariant formulation of infrared physics beyond the massless case. The results generalize the connection between soft theorems, symmetries, and memory to massive QED and potentially the Standard Model, with practical implications for organizing infrared effects in scattering processes.

Abstract

The soft photon theorem in U(1) gauge theories with only massless charged particles has recently been shown to be the Ward identity of an infinite-dimensional asymptotic symmetry group. This symmetry group is comprised of gauge transformations which approach angle-dependent constants at null infinity. In this paper, we extend the analysis to all U(1) theories, including those with massive charged particles such as QED.