The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology
arXiv:0709.4225 · doi:10.1088/0264-9381/25/5/055003
Abstract
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.
Latex, 12 pages
References in corpus (24)
- Background Independent Quantum Gravity: A Status Report
- Discreteness of area and volume in quantum gravity
- Quantum Nature of the Big Bang: Improved dynamics
- Quantum Theory of Gravity I: Area Operators
- Quantum Nature of the Big Bang
- Quantum Spin Dynamics (QSD)
- Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
- Loop Quantum Cosmology
- Partial observables
- Loop quantum cosmology of k=1 FRW models
- Differential Geometry on the Space of Connections via Graphs and Projective Limits
- Partial and Complete Observables for Hamiltonian Constrained Systems
- Partial and Complete Observables for Canonical General Relativity
- Isotropic Loop Quantum Cosmology
- The Phoenix Project: Master Constraint Programme for Loop Quantum Gravity
- QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
- A length operator for canonical quantum gravity
- Closed FRW model in Loop Quantum Cosmology
- Closed formula for the matrix elements of the volume operator in canonical quantum gravity
- Reduced Phase Space Quantization and Dirac Observables
- Quantum Theory of Geometry III: Non-commutativity of Riemannian Structures
- Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity
- Spectral Analysis of the Volume Operator in Loop Quantum Gravity
- Simplifying the spectral analysis of the volume operator
Cited by in corpus (6)
- Loop Quantum Cosmology: A Status Report
- Loop Quantum Cosmology: An Overview
- Cosmic recall and the scattering picture of Loop Quantum Cosmology
- Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
- Physical time and other conceptual issues of QG on the example of LQC
- The geometry and entanglement entropy of surfaces in loop quantum gravity