New Symmetries of Massless QED

Abstract

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 $\epsilon (z,\bar{z})$ on the conformal sphere at future null infinity (${\mathcal{I}}^{+}$) but are independent of the retarded time. The value of $\epsilon$ at past null infinity (${\mathcal{I}}^{-}$) is determined from that on ${\mathcal{I}}^{+}$ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The $\epsilon \ne$ 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.

17 pages, v2: typos in equations corrected

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