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

TL;DR

This paper studies Green's functions connecting null to time-like infinity in Minkowski spacetime, elucidating their role in large gauge symmetries and asymptotic structures, and verifying their consistency with Poincare symmetries.

Contribution

It provides a detailed analysis of Green's functions for large gauge parameters, establishing their hierarchy and their role in connecting boundary symmetries at null and time-like infinity.

Findings

Green's functions form a hierarchy describing boundary to bulk propagators.

They map Poincare group at null infinity to that at time-like infinity.

Verification of consistency with large gauge symmetries and asymptotic structures.

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.