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

TL;DR

The paper examines an infinite hierarchy of soft-photon theorems in tree-level massless QED and demonstrates a corresponding tower of asymptotic conservation laws arising from the radiative data at null and spatial infinity.It explicitly proves the equivalence between the subleading soft theorem and its associated asymptotic charge, and provides substantial evidence for the same correspondence at the sub-subleading level, while outlining a general conjecture for all higher orders.By relating these charges to Newman–Penrose charges and constructing a classical conservation proof via spatial infinity, the work clarifies how infrared structure in gauge theories can be encoded as boundary data, with implications for both classical and quantum formulations.The results suggest a deeper algebraic and geometric organization of soft theorems and asymptotic charges in gauge theories, and motivate future extensions to gravity and loop-corrected amplitudes.

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.