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We derive for generally covariant theories the generic dependency ofobservables on the original fields, corresponding to coordinate-dependent gaugefixings. This gauge choice is equivalent to a choice of intrinsically definedcoordinates accomplished with the aid of spacetime scalar fields. With ourapproach we make full contact with, and give a new perspective to, the"evolving constants of motion" program. We are able to directly derive genericproperties of observables, especially their dynamics and their Poisson algebrain terms of Dirac brackets, extending earlier results in the literature. Wealso give a new interpretation of the observables as limits of canonical maps.

Revisiting observables in generally covariant theories in the light of gauge fixing methods