Asymptotic charges in massless QED revisited: A view from Spatial Infinity

TL;DR

This paper demonstrates that in massless QED, the hierarchy of soft photon theorems at tree level corresponds to a hierarchy of asymptotic conservation laws, linking soft theorems to asymptotic charges and Newman-Penrose charges.

Contribution

It explicitly proves the equivalence between soft photon theorems hierarchy and asymptotic conservation laws in massless QED, extending previous results and clarifying their relationship.

Findings

Hierarchy of soft photon theorems corresponds to conservation laws.

Explicit proof for sub-subleading soft photon theorem case.

Connection between asymptotic charges and Newman-Penrose charges.

Abstract

Hamada and Shiu have recently shown that tree level amplitudes in QED satisfy an infinite hierarchy of soft photon theorems, the first two of which are Weinberg and Low's theorems respectively. In this paper we propose that in tree level massless QED, this entire hierarchy is equivalent to a hierarchy of (asymptotic) conservation laws. We prove the equivalence explicitly for the case of sub-subleading soft photon theorem and give substantial evidence that the equivalence continues to hold for the entire hierarchy. Our work also brings out the (complimentary) relationship between the asymptotic charges associated to soft theorems and the well known Newman-Penrose charges.