Symmetries of free massless particles and soft theorems

TL;DR

This paper explores the relationship between soft theorems and symmetries for massless particles, using a basis of states on null infinity and focusing on leading soft photon and graviton theorems.

Contribution

It introduces a basis of massless states on null infinity and investigates how soft theorems relate to symmetries within this framework.

Findings

Soft photon theorem linked to U(1) Kac-Moody symmetry

Soft graviton theorem related to supertranslations

Preliminary steps towards connecting soft theorems with asymptotic symmetries

Abstract

In an earlier paper we have constructed a basis of massless single particle quantum states which transform in the unitary principal series representation of the four dimensional Lorentz group. The S-matrix written in this basis gives rise to the Mellin transformed amplitude of Pasterski-Shao-Strominger and its generalization. In this basis the particle can be thought of as living on the null-infinity in the Minkowski space. In this paper we take some preliminary steps to see how the connection between soft theorems and symmetries work out in this picture. For simplicity we consider only the leading soft photon and soft graviton theorems which are related to U(1) Kac-Moody and supertranslations.