Partial and Complete Observables for Hamiltonian Constrained Systems

TL;DR

This paper extends the concepts of partial and complete observables for gauge systems, providing methods to construct Dirac observables in Hamiltonian constrained systems and relating them to background independent theories.

Contribution

It generalizes the framework of partial and complete observables to systems with multiple gauge degrees of freedom and explores their relation to Kuchař's Bubble Time Formalism.

Findings

Developed methods to calculate Dirac observables in gauge systems.

Established a connection between partial/complete observables and Bubble Time Formalism.

Analyzed gauge actions and Poisson brackets on the space of observables.

Abstract

We will pick up the concepts of partial and complete observables introduced by Rovelli in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are developed. For background independent field theories we will show that partial and complete observables can be related to Kucha\v{r}'s Bubble Time Formalism. Moreover one can define a non-trivial gauge action on the space of complete observables and also state the Poisson brackets of these functions. Additionally we will investigate, whether it is possible to calculate Dirac observables starting with partially invariant partial observables, for instance functions, which are invariant under the spatial diffeomorphism group.