Null to time-like infinity Green's functions for asymptotic symmetries in Minkowski spacetime

TL;DR

The paper develops a unified framework for asymptotic symmetries in Minkowski space that extends soft-theorem–Ward-identity connections to massive particles. By modeling time-like infinity as a unit hyperboloid and constructing boundary-to-bulk Green's functions, it provides explicit kernels for U(1) large gauge transformations, supertranslations, and sphere-vector symmetries that map null infinity data to time-like infinity. It then links these Green's functions to soft factors and verifies that the Poincaré subgroup of the generalized BMS group acts consistently across null and time-like infinities, recovering translations, boosts, and rotations. This work offers a concrete, calculable bridge between asymptotic symmetries and soft physics for massive scattering in flat spacetime, with potential extensions to nonlinear gravity.

Abstract

We elaborate on the Green's functions that appeared in [1,2] when generalizing, from massless to massive particles, various equivalences between soft theorems and Ward identities of large gauge symmetries. We analyze these Green's functions in considerable detail and show that they form a hierarchy of functions which describe `boundary to bulk' propagators for large $U(1)$ gauge parameters, supertranslations and sphere vector fields respectively. As a consistency check we verify that the Green's functions associated to the large diffeomorphisms map the Poincare group at null infinity to the Poincare group at time-like infinity.