# Asymptotic symmetries of electromagnetism at spatial infinity

## TL;DR

This paper investigates the asymptotic symmetries of Maxwell theory at spatial infinity using Hamiltonian formalism, revealing infinite-dimensional gauge symmetries with non-zero charges and extending the symplectic structure to include boundary effects.

## Contribution

It provides a detailed Hamiltonian analysis of asymptotic electromagnetic symmetries at spatial infinity, including boundary conditions, surface degrees of freedom, and magnetic monopoles.

## Key findings

- Identifies angle-dependent $u(1)$ gauge symmetries at spatial infinity.
- Shows these symmetries have non-vanishing charges.
- Extends the Hamiltonian framework to include boundary modifications.

## Abstract

We analyse the asymptotic symmetries of Maxwell theory at spatial infinity through the Hamiltonian formalism. Precise, consistent boundary conditions are explicitly given and shown to be invariant under asymptotic angle-dependent $u(1)$-gauge transformations. These symmetries generically have non-vanishing charges. The algebra of the canonical generators of this infinite-dimensional symmetry with the Poincar\'e charges is computed. The treatment requires the addition of surface degrees of freedom at infinity and a modification of the standard symplectic form by surface terms. We extend the general formulation of well-defined generators and Hamiltonian vector fields to encompass such boundary modifications of the symplectic structure. Our study covers magnetic monopoles.