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Mathematical structure of loop quantum cosmology
Open accessAbstract
Applications of Riemannian quantum geometry to cosmology have had notable successes.In particular, the fundamental discreteness underlying quantum geometry has led to a natural resolution of the big bang singularity.However, the precise mathematical structure underlying loop quantum cosmology and the sense in which it implements the full quantization program in a symmetry reduced model has not been made explicit.The purpose of this paper is to address these issues, thereby providing a rmer mathematical and conceptual foundation to the subject.
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Cites
Kiefer, C. (2004) · Cited by 2,981
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951
Self-citationNew Variables for Classical and Quantum Gravity
Ashtekar, A. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.2244 · Cited by 1,663
Self-citationDiscreteness 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×
“In quantum geometry, on the other hand, the area operator (of an open surface) has a lowest eigenvalue ao = ( √ 3γ)/4 l(2)Pl [17,30] suggesting that it is physically inappropriate to try to localize Fab on arbitrarily small surfaces.”
BackgroundNew Hamiltonian formulation of general relativity
Ashtekar, A. (1987) · Physical Review D · doi:10.1103/physrevd.36.1587 · Cited by 1,119
Self-citationQuantum geometry and black hole entropy
Ashtekar, A., Baez, J., Corichi, A., & Krasnov, K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.904 · Cited by 1,105
Self-citationQuantum theory of geometry: I. Area operators
Ashtekar, A., & Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1a/006 · Cited by 852
Self-citationAbsence of a Singularity in Loop Quantum Cosmology
Bojowald, M. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5227 · Cited by 769
Spin networks and quantum gravity
Rovelli, C., & Smolin, L. (1995) · Physical Review D · doi:10.1103/physrevd.52.5743 · Cited by 629
Quantum geometry of isolated horizons and black hole entropy
Ashtekar, A., Baez, J. C., & Krasnov, K. (2000) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2000.v4.n1.a1 · Cited by 580
Self-citation
Flagged first, then by citations
Research works printed but not linked: 10
- [3]3. M. Bojowald, Absence o f singularity in loop quantum cosmology, Phys. Rev. Lett., 86 (2001), 5227{5230.
- [5]5. M. Bojowald, Ination from quantum geometry, Phys. Rev. Lett., 89 (2002), 261301.
- [9]9. A. Ashtekar and J. Lewandowski, Representation theory of analytic holonomy algebras, in `Knots and Quantum Gravity', edired by J.C. Baez, Oxford U. Press, Oxford 1994.
- [12]12. A. Ashtekar and J. Lewandowski, Projective techniques and functional integration, Jour. Math. Phys., 36 (1995), 2170-2191.
- [13]13. A. Ashtekar and J. Lewandowski, Dierential geometry on the space of connections using projective techniques, Jour. Geo. & Phys., 17 (1995), 191{230.
- [15]15. QSD V : Quantum gravity as the natural regulator of matter quantum eld theories, Class. Quant. Grav., 15 (1998), 1281{1314.
- [21]21. J. Lewandowski and A. Okolow, Dieomorphism covariant representa- tions of the holonomy-ux star-algebra, gr-qc/0302059. · arXiv
- [25]25. J. C. Baez, Spin networks in non-perturbative quantum gravity, i n T h e Interface of Knots and Physics', edited by Kauman, L. (American Mathematical Society, P r o vidence, 1996) pp. 167{203 Spin networks in gauge theory, Adv. Math. 117 (1996), 253{272.
- [38]38. A. Ashtekar, J. Lewandowski and H. Sahlmann, Polymer and Fock rep- resentations for a Scalar eld, Class. Quantum Grav. 20 (2003), L1{11.
- [40]40. A. Erd+ elyi, Asymptotic expansions, Chapter II (Dover, New York, 1956).
Cited by
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“To summarize, the Hamiltonian constraint will be improved by implementing the physical idea of [4] in a more satisfactory manner.”
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Stepping out of homogeneity in loop quantum cosmology
Carlo Rovelli, C., & Vidotto, F. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/22/225024 · Cited by 101
Metadata
- Authors
- Ashtekar, A., Bojowald, M., & Lewandowski, J.
- Affiliations
- Pennsylvania State University (US)
- Venue
- Advances in Theoretical and Mathematical Physics
- Publisher
- International Press of Boston
- Published
- 2003
- Volume
- 7
- Issue
- 2
- Pages
- 233-268
- ISSN
- 1095-0753 (ISSN-L)
- 1095-0761
- OpenAlex
- W2101065856
- Cited by
- 762
- References
- 38
- Citations by year
- 2026: 14 · 2025: 30 · 2024: 24 · 2023: 26 · 2022: 21 · 2021: 37 · 2020: 35 · 2019: 34 · 2018: 27 · 2017: 21 · 2016: 36 · 2015: 31 · 2014: 31 · 2013: 44 · 2012: 48
- FWCI
- 25.23
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Advances in Theoretical and Mathematical Physics (publishedVersion)
- Funders
- National Science Foundation (0090091)
- University of Pennsylvania
- Pennsylvania State University
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy 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, Big Bang singularity resolution, discrete spacetime, mathematical structures
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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