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Cited by 762Noncommutative and Quantum Gravity TheoriesCosmology and Gravitation TheoriesRelativity and Gravitational Theory

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Mathematical structure of loop quantum cosmology

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Ashtekar, Abhay, Bojowald, Martin, Lewandowski, Jerzy·2003·Advances in Theoretical and Mathematical Physics
DOI 10.4310/atmp.2003.v7.n2.a2
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Abstract

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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Research works printed but not linked: 10

  1. [3]3. M. Bojowald, Absence o f singularity in loop quantum cosmology, Phys. Rev. Lett., 86 (2001), 5227{5230.
  2. [5]5. M. Bojowald, Ination from quantum geometry, Phys. Rev. Lett., 89 (2002), 261301.
  3. [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.
  4. [12]12. A. Ashtekar and J. Lewandowski, Projective techniques and functional integration, Jour. Math. Phys., 36 (1995), 2170-2191.
  5. [13]13. A. Ashtekar and J. Lewandowski, Dierential geometry on the space of connections using projective techniques, Jour. Geo. & Phys., 17 (1995), 191{230.
  6. [15]15. QSD V : Quantum gravity as the natural regulator of matter quantum eld theories, Class. Quant. Grav., 15 (1998), 1281{1314.
  7. [21]21. J. Lewandowski and A. Okolow, Dieomorphism covariant representa- tions of the holonomy-ux star-algebra, gr-qc/0302059. · arXiv
  8. [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.
  9. [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.
  10. [40]40. A. Erd+ elyi, Asymptotic expansions, Chapter II (Dover, New York, 1956).

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Metadata

Authors
Ashtekar, A., Bojowald, M., & Lewandowski, J.
Affiliations
Pennsylvania State University (US)
ORCID
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
DOI
10.4310/atmp.2003.v7.n2.a2
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
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

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