Partial and complete observables for Hamiltonian constrained systems

2004/11/02 by Bianca Dittrich, B. Dittrich · 10 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantum gravity #Cosmology and Gravitation Theories #Diffeomorphism #Gauge theory #Hamiltonian (control theory) #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observable #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Theoretical physics #Wheeler–DeWitt equation #gr-qc

paper · pdf · doi:10.1007/s10714-007-0495-2

published as Gen.Rel.Grav.39:1891-1927,2007 · 38 pages

arxiv created 2004/11/02 · openalex publication_date 2007/08/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Kuchař'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.

Citations

• Towards a unified description of the four interactions in terms of Dirac-Bergmann observables
• Quantization of Gauge Systems
• Gravitational Observables and Local Symmetries
• TIME AND INTERPRETATIONS OF QUANTUM GRAVITY

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