Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
arXiv:gr-qc/0507037 · doi:10.1088/0264-9381/23/18/012
Abstract
In this paper we provide the techniques and proofs for the resuls presented in our companion paper concerning the consistency check on volume and triad operator quantisation in Loop Quantum Gravity.
67 pages, 6 figures, 36 pages paper, 31 pages appendix
References in corpus (9)
- Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
- Testing the Master Constraint Programme for Loop Quantum Gravity I. General Framework
- Spectral Analysis of the Volume Operator in Loop Quantum Gravity
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
- Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
- Testing the Master Constraint Programme for Loop Quantum Gravity IV. Free Field Theories
- On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories
- Testing the Master Constraint Programme for Loop Quantum Gravity V. Interacting Field Theories
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- Loop Quantum Gravity: An Inside View
- On the regularization ambiguities in loop quantum gravity
- The length operator in Loop Quantum Gravity
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- Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity II
- Consistency Check on Volume and Triad Operator Quantisation in Loop Quantum Gravity I
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- Towards an Anomaly-Free Quantum Dynamics for a Weak Coupling Limit of Euclidean Gravity
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- Mathematical Structure of Loop Quantum Cosmology: Homogeneous Models
- From Classical To Quantum Gravity: Introduction to Loop Quantum Gravity
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- Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States
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- Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse
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- Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
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