# A Poisson Algebra for Abelian Yang-Mills Fields on Riemannian Manifolds with Boundary

## TL;DR

This paper introduces a Poisson algebra structure for abelian Yang-Mills fields on Riemannian manifolds with boundary, defining gauge-invariant observables linked to conserved currents and their brackets.

## Contribution

It develops a new algebraic framework for abelian Yang-Mills observables on Riemannian manifolds with boundary, incorporating a Poisson structure based on presymplectic currents.

## Key findings

- Defined a family of gauge-invariant observables
- Established a Poisson bracket using presymplectic currents
- Connected observables to conserved currents in the region

## Abstract

We define a family of observables for abelian Yang-Mills fields associated to compact regions $U \subseteq M$ with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the integration of gauge invariant conserved current along admissible hypersurfaces contained in the region. The Poisson bracket uses the integration of a canonical presymplectic current.