Asymptotic $U(1)$ charges at spatial infinity

TL;DR

This work presents a unified framework for large U(1) gauge symmetries in Minkowski space by analyzing Maxwell theory at spatial infinity via the space-like hyperboloid, establishing conservation laws that interpolate between charges defined at past and future null infinity. It constructs a covariant phase-space on constant-\tau slices to formulate canonical large-U(1) charges at spatial infinity, showing these charges reproduce the known i± charges and are governed by a canonical pair (\lambda, ψ) on the hyperboloid. The analysis also incorporates magnetic duals, yielding conserved magnetic charges with a similar structure and a clean dual interpretation. Overall, the paper provides a coherent, time-reparametrization-invariant picture linking null and spatial infinity charges, with potential implications for gravity and holography.

Abstract

Large gauge symmetries in Minkowski spacetime are often studied in two distinct regimes: either at asymptotic (past or future) times or at spatial infinity. By working in harmonic gauge, we provide a unified description of large gauge symmetries (and their associated charges) that applies to both regimes. At spatial infinity the charges are conserved and interpolate between those defined at the asymptotic past and future. This explains the equality of asymptotic past and future charges, as recently proposed in connection with Weinberg's soft photon theorem.