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

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 consid- erable 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.