New symmetries of massless QED

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U (1) gauge transformations that asymptotically approach an arbitrary function (z, z) on the conformal sphere at future null infinity () but are independent of the retarded time. The value of ε at past null infinity () is determined from that on by the condition that it take the same value at either end of any light ray crossing Minkowski space. The ε ≠ constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U (1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.