New Symmetries of Massless QED

TL;DR

This paper uncovers an infinite set of new symmetries in massless QED linked to large gauge transformations at null infinity, connecting them to soft photon theorems and Goldstone modes.

Contribution

It identifies an infinite-dimensional symmetry group in massless QED and relates it to soft photon theorems and spontaneous symmetry breaking.

Findings

Large gauge transformations form an infinite symmetry group.

Associated Goldstone modes are zero-momentum photons.

Ward identities correspond to soft photon theorems.

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