Loop quantum cosmology: II. Volume operators
Open accessAbstract
Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly. It is observed that the stronger the symmetry conditions are the smaller is the volume spectrum, which can be interpreted as level splitting due to broken symmetries. Some implications for quantum cosmology are presented.
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The Hamiltonian constraints for cosmological models can be quantized with some adaptations to the symmetry.
“Following the basic steps of the quantization in the full theory [11], the Hamiltonian constraints for cosmological models can be quantized with some adaptations to the symmetry [12].”
From Absence of a Singularity in Loop Quantum Cosmology (2001) · cites this paper as [11]
Bianchi class A models constitute all homogeneous models with a freely acting symmetry group (F={1}) that can be treated in a Hamiltonian formulation; Bianchi class B models violate the principle of symmetric criticality.
“Bianchi class A models constitute all homogeneous models with a freely acting symmetry group (F = {1}) which can be treated in a Hamiltonian formulation (Bianchi class B models violate the principle of symmetric criticality [25,26]).”
From Loop quantum cosmology: I. Kinematics (2000) · cites this paper as [26]
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Cites
Discreteness of area and volume in quantum gravity
Rovelli, C., & Smolin, L. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00150-q · Cited by 1,365 · cited 1× · see citing works
“The momenta conjugate to the connections above are invariant (with respect to the Saction) density-weighted dreibeine given by Eai = √ g0 p I iX a I in terms of left invariant vector fields XI obeying ω I(XJ) = δ I J .”
MethodKinematical Hilbert spaces for fermionic and Higgs quantum field theories
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/6/006 · Cited by 184 · see citing works
What is the geometry of superspace?
Giulini, D. (1995) · Physical Review D · doi:10.1103/physrevd.51.5630 · Cited by 74 · see citing works
Simplifying the spectral analysis of the volume operator
Loll, R. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00334-9 · Cited by 27 · see citing works
The Area Operator in the Spherically Symmetric Sector of Loop Quantum Gravity
Bojowald, M., & Kastrup, H. A. (1999) · CERN Document Server (European Organization for Nuclear Research) · doi:10.48550/arxiv.hep-th/9907043 · Cited by 7 · see citing works
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Research works printed but not linked: 5
- Bojowald M and Kastrup H A 1999 Quantum symmetry reduction for diffeomorphism invariant theories of connections Preprint hep-th/9907042 · arXiv
- Bojowald M Loop quantum cosmology III: Wheeler-DeWitt operators Preprint in preparation
- Kobayashi S and Nomizu K 1963 Foundations of Differential Geometry vol 1 (New York: Wiley) ch II.11
- Kobayashi S and Nomizu K 1969 Foundations of Differential Geometry vol 2 (New York: Wiley) ch X
- Bröcker T and tom Dieck T 1995 Representations of compact Lie groups (Berlin: Springer)
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Bojowald, M. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-11 · Cited by 723 · see citing works
Self-citationSymmetry reduction for quantized diffeomorphism-invariant theories of connections
Bojowald, M., & Kastrup, H. A. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/15/311 · Cited by 168 · see citing works
Self-citationLoop quantum cosmology: I. Kinematics
Bojowald, M. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/6/312 · Cited by 125 · see citing works
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- Authors
- Bojowald, M.
- Affiliations
- RWTH Aachen University (DE)
- Corresponding author
- Bojowald, Martin
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2000-03-03
- Volume
- 17
- Issue
- 6
- Pages
- 1509-1526
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2066934361
- Cited by
- 85
- References
- 5
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 1 · 2023: 4 · 2022: 2 · 2020: 2 · 2019: 2 · 2017: 2 · 2016: 4 · 2015: 1 · 2014: 1 · 2013: 1 · 2012: 5
- FWCI
- 4.97
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- loop quantum cosmology, volume operator, quantum cosmology, isotropic cosmological models, symmetry breaking, energy level splitting, rotational symmetry
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