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

The DOI matches its Crossref record; 43 of the 43 references it cites were found in a registry or an index.

Mathematical structure of loop quantum cosmology

Open access
Ashtekar, Abhay, Bojowald, Martin, Lewandowski, Jerzy·2003·Advances in Theoretical and Mathematical Physics
DOI 10.4310/atmp.2003.v7.n2.a2
Open this paper in CoChat — free accountOpen PDF

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.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.4310/atmp.2003.v7.n2.a2

Cites

43 of 43 references verified0 citation errors · 0 not checkable

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Flagged first, then by citations

Show all 38 references

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).

Cited by

Sorted by citations

Items 301–400 of 741

Related

See all

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

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.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review