A note on asymptotic symmetries and soft-photon theorem

Abstract

We use the asymptotic data at conformal null-infinity $\mathcal{I}$ to formulate Weinberg's soft-photon theorem for Abelian gauge theories with massless charged particles. We show that the angle-dependent gauge transformations at $\mathcal{I}$ 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 the 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 ${\mathcal{I}}^{+}$ and ${\mathcal{I}}^{-}$ respectively, Strominger has shown that a certain diagonal subgroup ${\mathcal{G}}_{diag}\subset {\mathcal{G}}_{+}\times {\mathcal{G}}_{-}$ 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.

arXiv comment21 pages, 0 figures, references added, acknowledgments updated. This version accepted for publication in JHEP

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