Low’s Subleading Soft Theorem as a Symmetry of QED

It was shown by Low in the 1950s that the subleading terms of soft-photon $S$-matrix elements obey a universal linear relation. In this Letter, 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.