The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology

Details The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology

2007-09-26

arxiv.org/abs/0709.4225v2

Class.Quant.Grav.25:055003,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 12 pages

Scientific paper

10.1088/0264-9381/25/5/055003

This letter is motivated by the recent papers by Dittrich and Thiemann and, respectively, by Rovelli discussing the status of Quantum Geometry in the dynamical sector of Loop Quantum Gravity. Since the papers consider model examples, we also study the issue in the case of an example, namely on the Loop Quantum Cosmology model of space-isotropic universe. We derive the Rovelli-Thiemann-Ditrich partial observables corresponding to the quantum geometry operators of LQC in both Hilbert spaces: the kinematical one and, respectively, the physical Hilbert space of solutions to the quantum constraints. We find, that Quantum Geometry can be used to characterize the physical solutions, and the operators of quantum geometry preserve many of their kinematical properties.

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