Relational Evolution of Observables for Hamiltonian-Constrained Systems

Understand

Evolution of systems in which Hamiltonians are generators of gauge transformations is a notion that requires more structure than the canonical theory provides.

• We identify and study this additional structure in the framework of relational observables ("partial observables").
• We formulate necessary and sufficient conditions for the resulting evolution in the physical phase space to be a symplectomorphism.
• We give examples which satisfy those conditions and examples which do not.