Low's Subleading Soft Theorem as a Symmetry of QED

TL;DR

This work reframes Low's subleading soft photon theorem in massless QED as an infinitesimal S-matrix symmetry generated by a vector field on the conformal sphere at null infinity. It constructs associated soft and hard charges, ${rak Q}^ ext{±}_S$ and ${rak Q}^ ext{±}_H$, whose combination yields a Ward identity that reproduces the subleading soft behavior. The charges admit local boundary expressions on ${rak I}^ ext{±}$ and connect to magnetic dipole data, suggesting a local generalization of dipole charges beyond standard gauge symmetries. The results hint at a richer structure of soft symmetries in massless QED, with potential links to deeper algebraic structures and extensions to massive theories, meriting further exploration.

Abstract

It was shown by F. Low in the 1950s that the subleading terms of soft photon S-matrix elements obey a universal linear relation. In this paper we give a new interpretation to this old relation, for the case of massless QED, as an infinitesimal symmetry of the S-matrix. The symmetry is shown to be locally generated by a vector field on the conformal sphere at null infinity. Explicit expressions are constructed for the associated charges as integrals over null infinity and shown to generate the symmetry. These charges are local generalizations of electric and magnetic dipole charges.