2+1 lattice gravity
Abstract
This is a theory of 2+1 gravity with a spacelike lattice and continuous time. It is derived from the Chern-Simons formulation of 2+1 gravity, in which the frame vectors are canonically conjugate to the SO(2, 1) connection. Dirac brackets are computed for the corresponding lattice variables: the link 3-vectors and the SO(2, 1) matrices which define parallel transport across the boundary between neighbouring faces. There is a set of first-class constraints, which state that the lattice analogues of torsion and curvature vanish locally. These generate local Lorentz rotations and independent translations of each lattice site. One finds the same complete set of observables as in the Chern-Simons formulation.
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A related first-order Hamiltonian lattice model has been studied by Waelbroeck et al.
“A related first-order Hamiltonian lattice model has been studied by Waelbroeck et al. [266, 267, 268, 270].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [266]
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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Regge calculus: a brief review and bibliography
Williams, R. M., & Tuckey, P. A. (1992) · Classical and Quantum Gravity · doi:10.1088/0264-9381/9/5/021 · Cited by 175 · see citing works
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
- Authors
- Waelbroeck, H.
- Affiliations
- The University of Texas at Austin (US)
- Corresponding author
- Waelbroeck, H
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1990-05-01
- Volume
- 7
- Issue
- 5
- Pages
- 751-769
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2082585934
- Cited by
- 37
- References
- 2
- Citations by year
- 2012: 1
- FWCI
- 1.75
- Type
- journal article
- Language
- en
- Open access
- closed
- 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
- three-dimensional gravity, lattice gravity, Chern-Simons gravity, Dirac brackets, first-class constraints, parallel transport, lattice gauge theory, discrete spacetime
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