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

Abstract

We define a family of observables for abelian Yang-Mills fields associated to compact regions U ⊆ 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 multisymplectic current.