Partial and complete observables for Hamiltonian constrained systems
Abstract
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 BubbleTime Formalism (J Math Phys, 13:768, 1972). Moreover one can define a nontrivial 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.
 Publication:

General Relativity and Gravitation
 Pub Date:
 November 2007
 DOI:
 10.1007/s1071400704952
 arXiv:
 arXiv:grqc/0411013
 Bibcode:
 2007GReGr..39.1891D
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 38 pages