2+1 quantum gravity as a toy model for the 3+1 theory
Open accessAbstract
2+1 Einstein gravity is used as a toy model for testing a program for nonperturbative canonical quantisation of the 3+1 theory. The program can be successfully implemented in the model and leads to a surprisingly rich quantum theory.
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.
Integrity signals
Registry
Cites
Statistics
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.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For the torus universe, the loop transform can be obtained explicitly and written as a simple integral transform.
“For the torus universe, this “loop transform” can be obtained explicitly [26, 29, 192], and written as a simple integral transform.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [29]
For the torus universe, a complete, explicit description of loop representation states is possible.
“The loop representation is complicated by the existence of Mandelstam identities [190] among holonomies of loops, but for the case of the torus universe, a complete, explicit description of the states is again possible [26, 29].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [29]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
The citation lists haven’t been fetched yet
References 13 · Cited by 165
Research works printed but not linked: 8
- Rovelli C and Smolin L 1988 Phys. Rev. Lett. 61 1155; 1989 Nucl. Phys. B in press
- Ashtekar A and Lee J 1989 Syracuse preprint
- Ashtekar A, Rovelli C and Smolin L 1989 Syracuse preprint
- Husain V and Smolin L Nucl. Phys. B in press Kodama H 1988 Prog. Theor. Phys. 80 1024
- Ashtekar A, Romano J D and Tate R S 1989 Phys. Reo. D in press Part I1 Birkhauser)
- I l l Carlip S 1989 IAS preprint IASSNS-HEP-89/4
- I21 Martin S 1989 Princeton preprint PUPT-1120 [I31
- Ashtekar A and Romano J 1989 Phys. Lett. B in press [I41 Samuel J 1987 Pramana 28 U 2 9
- Authors
- Ashtekar, A., Husain, V, Rovelli, C., Samuel, J., & Smolin, L.
- Affiliations
- Syracuse University (US)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1989-10-01
- Volume
- 6
- Issue
- 10
- Pages
- L185-L193
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1965866051
- Cited by
- 165
- References
- 13
- Citations by year
- 2025: 2 · 2024: 3 · 2023: 2 · 2021: 2 · 2020: 2 · 2019: 1 · 2016: 2 · 2015: 1 · 2014: 2 · 2013: 2 · 2012: 2
- FWCI
- 15.25
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- toy model, quantum gravity
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
