Low's Subleading Soft Theorem as a Symmetry of QED

TL;DR

This paper reinterprets Low's subleading soft photon theorem in massless QED as a new symmetry of the S-matrix, generated by charges at null infinity, extending the understanding of electromagnetic symmetries.

Contribution

It provides a novel symmetry interpretation of Low's theorem in massless QED, with explicit charge expressions at null infinity.

Findings

The subleading soft photon theorem is a symmetry of the S-matrix.

Charges are constructed as integrals over null infinity.

Charges generalize electric and magnetic dipole moments.

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.