Asymptotic symmetries of QED and Weinberg's soft photon theorem

TL;DR

The paper extends the connection between soft photon theorems and asymptotic Ward identities to massive charges in scalar QED by defining time-like infinity on a hyperboloid and constructing an augmented asymptotic phase space. It shows that angle-dependent large U(1) gauge transformations act consistently on this space, yielding Ward identities that are equivalent to Weinberg's soft photon theorem. The analysis hinges on a Lorenz-gauge formulation and a precise decomposition into hard and soft charges, with a constructive kernel linking sphere data to hyperboloid data. This work paves the way for similar treatments of soft theorems in gravity with massive matter and illuminates the role of time-like infinity in infrared structure.

Abstract

Various equivalences between so-called soft theorems which constrain scattering amplitudes and Ward identities related to asymptotic symmetries have recently been established in gauge theories and gravity. So far these equivalences have been restricted to the case of massless matter fields, the reason being that the asymptotic symmetries are defined at null infinity. The restriction is however unnatural from the perspective of soft theorems which are insensitive to the masses of the external particles. In this work we remove the aforementioned restriction in the context of scalar QED. Inspired by the radiative phase space description of massless fields at null infinity, we introduce a manifold description of time-like infinity on which the asymptotic phase space for massive fields can be defined. The "angle dependent" large gauge transformations are shown to have a well defined action on this phase space, and the resulting Ward identities are found to be equivalent to Weinberg's soft photon theorem.