A note on asymptotic symmetries and soft-photon theorem

Abstract

We use the asymptotic data at conformal null-infinity to formulate Weinberg’s soft-photon theorem for Abelian gauge theories with massless charged particles. We show that the angle-dependent gauge transformations at are not merely a gauge redundancy, instead they are genuine symmetries of the radiative phase space. In the presence of these symmetries, Poisson bracket between gauge potentials is not well-defined. This does not pose an obstacle for the quantization of the radiative phase space, which proceeds by treating the conjugate electric field as the fundamental variable. Denoting by $$ {\mathcal{G}}_{+} $$ and $$ {\mathcal{G}}_{-} $$ as the group of gauge transformations at and respectively, Strominger has shown that a certain diagonal subgroup $$ {\mathcal{G}}_{\mathrm{diag}}\subset {\mathcal{G}}_{+}\times {\mathcal{G}}_{-} $$ is the symmetry of the S-matrix and Weinberg’s soft-photon theorem is the corresponding Ward identity. We give a systematic derivation of this result for Abelian gauge theories with massless charged particles. Our derivation is a slight generalization of the existing derivations since it is applicable even when the bulk spacetime is not exactly flat, but is only “almost” Minkowskian.