Consistent Discretization and Loop Quantum Geometry
Open accessAbstract
We apply the "consistent discretization" approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism constraint to reduce its space of solutions and the constraint is preserved exactly under the discrete evolution. One ends up with a theory that has as physical space what is usually considered the kinematical space of loop quantum geometry, given by diffeomorphism invariant spin networks endowed with appropriate rigorously defined diffeomorphism invariant measures and inner products. The dynamics can be implemented as a unitary transformation and the problem of time explicitly solved or at least reduced to a numerical problem. We exhibit the technique explicitly in (2+1)-dimensional gravity.
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(2+1)-dimensional gravity has recently been examined as an arena in which to test a new partially discrete, constraint-free formulation of quantum gravity.
“Similarly, (2 + 1)-dimensional gravity has recently been examined as an arena in which to test for a new partially discrete, constraint-free formulation of quantum gravity [138].”
From Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe (2005) · cites this paper as [138]
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Ooguri, H. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90188-h · Cited by 76 · see citing works
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Research works printed but not linked: 8
- [3]R. Gambini, J. Pullin, Phys. Rev. Lett. 90, 021301 (2003) [arXiv:gr-qc/0206055]; C. Di Bartolo, R. Gambini, J. Pullin, · arXiv
- Classical and Quantum Gravity 19, 5475 (2002) [arXiv:gr-qc/0205123]. · arXiv
- [4]R. Gambini and J. Pullin, Class. Quant. Grav. 20, 3341 (2003) [arXiv:gr-qc/0212033]. · arXiv
- [5]R. Gambini, R. A. Porto and J. Pullin, "Discrete quantum gravity solution to the problem of time: a model" in "Recent developments in gravity: proceedings of the 10th Hellenic Relativity Conference", World Scientific, Singapore (2003) [arXiv:gr-qc/0302064]. · arXiv
- [6]R. Gambini, R. A. Porto and J. Pullin, Class. Quant. Grav. 21, L51 (2004) [arXiv:gr-qc/0305098]; New J. Phys. 6, 45 (2004) [arXiv:gr-qc/0402118]. · arXiv
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The Spin-Foam Approach to Quantum Gravity
Perez, A. (2013) · Living Reviews in Relativity · doi:10.12942/lrr-2013-3 · Cited by 677 · 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
- Gambini, R., & Pullin, J.
- Affiliations
- Universidad de la República de Uruguay (UY)
- Louisiana State University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-03-18
- Volume
- 94
- Issue
- 10
- Pages
- 101302-101302
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2013344137
- Cited by
- 31
- References
- 1
- Citations by year
- 2024: 1 · 2023: 3 · 2021: 5 · 2020: 3 · 2018: 6 · 2017: 1 · 2016: 2 · 2013: 1
- FWCI
- 1.68
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Civil War Book Review (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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
- loop quantum gravity, general relativity, diffeomorphism constraint, Hamiltonian constraint, spin networks, problem of time, three-dimensional gravity, unitary dynamics
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