Consistent Canonical Quantization of General Relativity in the Space of Vassiliev Invariants
Open accessAbstract
We present a quantization of the Hamiltonian and diffeomorphism constraint of canonical quantum gravity in the spin network representation. The novelty consists in considering a space of wave functions based on the Vassiliev invariants. The constraints are finite, well defined, and reproduce at the level of quantum commutators the Poisson algebra of constraints of the classical theory. A similar construction can be carried out in 2+1 dimensions leading to the correct quantum theory.
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Regularization choices for the scalar constraint have to be made and the result is not unique.
“Regularization choices have to be made and the result is not unique.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [136]
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Discreteness of area and volume in quantum gravity
Rovelli, C., & Smolin, L. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00150-q · Cited by 1,365 · see citing works
Quantum geometry and black hole entropy
Ashtekar, A., Baez, J., Corichi, A., & Krasnov, K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.904 · Cited by 1,105 · see citing works
Nonstandard optics from quantum space-time
Gambini, R., & Pullin, J. (1999) · Physical Review D · doi:10.1103/physrevd.59.124021 · Cited by 960 · see citing works
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- [6]R. Gambini, J. Pullin, 'Loops, knots, gauge theories and quantum gravity', Cambridge University Press, Cambridge (1996).
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Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951 · see citing works
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 geometry of isolated horizons and black hole entropy
Ashtekar, A., Baez, J. C., & Krasnov, K. (2000) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2000.v4.n1.a1 · Cited by 580 · see citing works
Finite spin-foam-based theory of three- and four-dimensional quantum gravity
Gambini, R., & Pullin, J. (2002) · Physical Review D · doi:10.1103/physrevd.66.024020 · Cited by 10 · see citing works
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- Authors
- Di Bartolo, C., Gambini, R., Griego, J., & Pullin, J.
- Affiliations
- Universidad de la República de Uruguay (UY)
- Pennsylvania State University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2000-03-13
- Volume
- 84
- Issue
- 11
- Pages
- 2314-2317
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2050063181
- Cited by
- 37
- References
- 3
- Citations by year
- 2018: 1 · 2017: 1 · 2014: 2 · 2013: 1 · 2012: 1
- FWCI
- 4.97
- 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
- canonical quantum gravity, Vassiliev invariants, spin networks, Hamiltonian constraint, diffeomorphism constraint, constraint algebra, wave functions, three-dimensional gravity, loop quantum gravity
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