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

TL;DR

This paper explores how gauge fixing methods influence the form and properties of observables in generally covariant theories, providing new insights into their dynamics and algebraic structure.

Contribution

It introduces a gauge fixing approach using spacetime scalar fields to analyze observables, extending previous results and connecting with the evolving constants of motion framework.

Findings

Derived the dependency of observables on original fields under gauge fixing.

Established properties of observables' dynamics and Poisson algebra.

Provided a new interpretation of observables as limits of canonical maps.

Abstract

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