Hamiltonian gauge theory with corners

In this talk I will focus on the (local) Hamiltonian formulation of gauge theories on manifolds with corners in the particular, yet common, case in which they admit an equivariant momentum map. In the presence of corners the momentum map splits into a part encoding “Cauchy data” or constraints, and a part encoding the “flux” across the corner. This decomposition plays an important role in the construction of the reduced phase space, and it turns out to be related to symplectic reduction in stages, adapted for the occasion to local group actions. The output of this analysis are natural Poisson structures associated to corner submanifolds (both on- and off-shell), leading to the concept of (classical) flux superselection sectors as their symplectic leaves. If time permits I will discuss how this picture relates to modern cohomological investigations of field theory within the Batalin-Vilkovisky formalism, and how this might suggest a road map to quantum superselection. This is a joint work with A. Riello.