General Relativity and Gravitation

, Volume 39, Issue 11, pp 1891–1927 | Cite as

Partial and complete observables for Hamiltonian constrained systems

  • B. DittrichEmail author
Research Article


We will pick up the concepts of partial and complete observables introduced by Rovelli in Conceptional Problems in Quantum Gravity, Birkhäuser, Boston (1991); Class Quant Grav, 8:1895 (1991); Phys Rev, D65:124013 (2002); Quantum Gravity, Cambridge University Press, Cambridge (2007) 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 (J Math Phys, 13:768, 1972). 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.


Phase Space Gauge Transformation Poisson Bracket Poisson Algebra Dirac Bracket 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.MPI f. GravitationsphysikAlbert-Einstein-InstitutGolm near PotsdamGermany
  2. 2.Perimeter Institute for Theoretical PhysicsWaterlooCanada

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