Observable currents and a covariant Poisson algebra of physical observables

Understand

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.