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 εzz¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varepsilon \left(z,\overline{z}\right) $$\end{document} 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.