  Observable currents are locally defined gauge invariant conserved currents;
physical observables may be calculated integrating them on appropriate
hypersurfaces. Due to the conservation law the hypersurfaces become irrelevant
up to homology, and the main objects of interest become the observable currents
them selves. Gauge inequivalent solutions can be distinguished by means of
observable currents. With the aim of modeling spacetime local physics, we work
on spacetime domains $U\subset M$ which may have boundaries and corners.
Hamiltonian observable currents are those satisfying ${\sf
d_v}F=-\iota_V\Omega_L+{\sf d_h}\sigma^F$ and a certain boundary condition. The
family of Hamiltonian observable currents is endowed with a bracket that gives
it a structure which generalizes a Lie algebra in which the Jacobi relation is
modified by the presence of a boundary term. If the domain of interest has no
boundaries the resulting algebra of observables is a Lie algebra. In the
resulting framework algebras of observable currents are associated to bounded
domains, and the local algebras obey interesting gluing properties. These
results are due to considering currents that defined only locally in field
space and to a revision of the concept of gauge invariance in bounded spacetime
domains. A perturbation of the field on a bounded spacetime domain is regarded
as gauge if: (i) the "first order holographic imprint" that it leaves in any
hypersurface locally splitting a spacetime domain into two subdomains is
negligible according to the linearized gluing field equation, and (ii) the
perturbation vanishes at the boundary of the domain. A current is gauge
invariant if the variation in them induced by any gauge perturbation vanishes
up to boundary terms.
