  I develop a theory of symplectic reduction that applies to bounded regions in
Yang-Mills theory and electromagnetism. In this theory gauge-covariant
superselection sectors for the electric flux through the boundary of the region
play a central role: within such sectors, there exists a natural, canonically
defined, symplectic structure for the reduced Yang-Mills theory. This
symplectic structure does not require the inclusion of any new degrees of
freedom. In the non-Abelian case, it also supports a family of Hamiltonian
vector fields, which I call "flux rotations," generated by smeared,
Poisson-non-commutative, electric fluxes. Since the action of flux rotations
affects the total energy of the system, I argue that flux rotations fail to be
dynamical symmetries of Yang-Mills theory restricted to a region. I also
consider the possibility of defining a symplectic structure on the union of all
superselection sectors. This in turn requires including additional boundary
degrees of freedom aka "edge modes." However, unless the new edge modes model a
material physical system located at the boundary of the region, I argue that
the phase space extension by edge modes is inherently ambiguous and
gauge-breaking.
