An algebraic interpretation of the Wheeler - DeWitt equation
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We make a direct connection between the construction of three-dimensional topological state sums from tensor categories and three-dimensional quantum gravity by noting that the discrete version of the Wheeler - DeWitt equation is exactly the pentagon for the associator of the tensor category - the Biedenharn - Elliott identity. A crucial role is played by an asymptotic formula relating 6j-symbols to rotation matrices given by Edmonds.
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A candidate for a discrete version of the Wheeler-DeWitt equation in three dimensions has been found, for which the Ponzano-Regge wave functions are solutions.
“A candidate for a discrete version of the Wheeler-DeWitt equation in three dimensions has been found [47], for which the Ponzano-Regge wave functions are solutions.”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [47]
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Cites
2 + 1 dimensional gravity as an exactly soluble system
Witten, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90143-5 · Cited by 2,562 · see citing works
General relativity without coordinates
Regge, T. (1961) · Il Nuovo Cimento · doi:10.1007/bf02733251 · Cited by 1,477 · see citing works
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Research works printed but not linked: 8
- Moussouris J P 1983 Quantum models of spacetime based on re-coupling theory DPhil Thesis Oxford University
- Barrett J W and Westbury B W 1993 Spherical categories Preprint hep-th/9310164 · arXiv
- Barrett J W and Westbury B W 1996 PL invariants of 3-manifolds Trans. Am. Math. Soc. 348 3997-4022
- Mac Lane S 1971 Categories for the Working Mathematician (Berlin: Springer)
- Hawking S W and Ellis G F R 1973 The Large Scale Structure of Space-time (Cambridge: Cambridge University Press)
- Sundermayer K 1982 Constrained Dynamics (Lecture Notes in Physics 169) (Berlin: Springer)
- Edmonds A R 1960 Angular Momentum in Quantum Mechanics (Princeton, NJ: Princeton University Press)
- Barrett J W 1995 Skein spaces and spin structures Preprint gr-qc/9512041 · arXiv
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Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe
Carlip, S. (2005) · Living Reviews in Relativity · doi:10.12942/lrr-2005-1 · Cited by 172 · see citing works
Dittrich, B., & Höhn, P. A. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/11/115009 · Cited by 69 · see citing works
- Authors
- Barrett, J. W., & Crane, L.
- Affiliations
- University of Nottingham (GB)
- Kansas State University (US)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1997-08-01
- Volume
- 14
- Issue
- 8
- Pages
- 2113-2121
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2026563675
- Cited by
- 31
- References
- 2
- Citations by year
- 2024: 1 · 2020: 1 · 2019: 1 · 2018: 3 · 2016: 1 · 2014: 1 · 2013: 3 · 2012: 4
- FWCI
- 0.93
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Engineering and Physical Sciences Research Council
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Wheeler-DeWitt equation, topological field theory, tensor categories, three-dimensional quantum gravity, associator, 6j symbols, rotation matrices, state sums
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