Quantum geometry and quantum gravity
Barbero G,J. Fernando +1 more
- 25 Jun 2008
- Vol. 1023, Iss: 1, pp 3-33
TL;DR: In this article, the authors give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians, focusing on conceptual issues concerning the relationship of the formalism with other more traditional approaches inspired in the treatment of the fundamental interactions in the standard model.
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Abstract: The purpose of this contribution is to give an introduction to quantum geometry and loop quantum gravity for a wide audience of both physicists and mathematicians. From a physical point of view the emphasis will be on conceptual issues concerning the relationship of the formalism with other more traditional approaches inspired in the treatment of the fundamental interactions in the standard model. Mathematically I will pay special attention to functional analytic issues, the construction of the relevant Hilbert spaces and the definition and properties of geometric operators: areas and volumes.
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Citations
A critical analysis of the cosmological implementation of Loop Quantum Gravity
TL;DR: In this article, a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (lQG) theory is offered.
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On Global One-Dimensionality proposal in Quantum General Relativity
L. A. Glinka
- 07 Aug 2008
TL;DR: In this article, the simple quantum gravity model, based on a new conjecture within the canonically quantized 3+1 general relativity, is presented, which states that matter fields are functionals of an embedding volume form only and reduces the quantum geometrodynamics.
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Global one-dimensionality conjecture within quantum general relativity
TL;DR: A simple quantum gravity model, based on a new conjecture within the canonically quantized 3 + 1 general relativity, is presented in this article, which states that matter fields are functionals of an embedding volume form only and reduces the quantum geometrodynamics.
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A critical analysis of the cosmological implementation of loop quantum gravity
TL;DR: In this paper, a critical discussion on the procedure by which Loop Quantum Cosmology (LQC) is constructed from the full Loop Quantum Gravity (lQG) theory is offered.
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Canonical and symplectic analysis for three dimensional gravity without dynamics
TL;DR: In this paper, a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed, and the complete structure of the constraints and the Dirac brackets are explicitly computed.
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