Reduced phase space quantization and Dirac observables

Journal article

Publication Details

Author(s): Thiemann T
Journal: Classical and Quantum Gravity
Publication year: 2006
Volume: 23
Journal issue: 4
Pages range: 1163-1180
ISSN: 0264-9381


In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint algebra with structure functions rather than structure constants. Here We use this framework and propose how to implement explicitly a reduced phase space quantization of a given system, at least in principle, without the need to Compute the gauge equivalence classes. The degree of practicality of this programme depends on the choice of the partial observables involved. The (multi-fingered) time evolution was shown to correspond to an automorphism on the set of Dirac observables, so generated and interesting representations of the latter will be those for which a suitable preferred Subgroup is realized unitarily. We sketch how Such a programme might look for general relativity. We also observe that the ideas by Dittrich can be used in order to generate constraints equivalent to those of the Hamiltonian constraints for general relativity such that they are spatially diffeomorphism invariant. This has the important Consequence that one can now quantize the new Hamiltonian constraints on the partially reduced Hilbert space of spatially diffeomorphism invariant states, just as for the recently proposed master constraint programme.

FAU Authors / FAU Editors

Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik

How to cite

Thiemann, T. (2006). Reduced phase space quantization and Dirac observables. Classical and Quantum Gravity, 23(4), 1163-1180.

Thiemann, Thomas. "Reduced phase space quantization and Dirac observables." Classical and Quantum Gravity 23.4 (2006): 1163-1180.


Last updated on 2018-10-08 at 19:53