On Types of Observables in Constrained Theories

The Kuchar observables notion is shown to apply only to a limited range of theories. Relational mechanics, slightly inhomogeneous cosmology and supergravity are used as examples that require further notions of observables. A suitably general notion of A-observables is then given to cover all of these cases. A' here stands for algebraic substructure’; A-observables can be defined by association with each closed algebraic substructure of a theory’s constraints. Both constrained algebraic structures and associated notions of A-observables form bounded lattices.