Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra
Open accessAbstract
In a companion paper we introduced a kinematical arena for the discussion of the constraints of canonical quantum gravity in the spin network representation based on Vassiliev invariants. In this paper we introduce the Hamiltonian constraint, extend the space of states to non-diffeomorphism invariant ``habitats'' and check that the off-shell quantum constraint commutator algebra reproduces the classical Poisson algebra of constraints of general relativity without anomalies. One can therefore consider the resulting set of constraints and space of states as a consistent theory of canonical quantum gravity.
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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 [135]
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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
Self-citationBF description of higher-dimensional gravity theories
Freidel, L., Krasnov, K., & Puzio, R. (1999) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1999.v3.n5.a3 · Cited by 137 · see citing works
Knot invariants as nondegenerate quantum geometries
Brügmann, B., Gambini, R., & Pullin, J. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.431 · Cited by 94 · see citing works
Self-citationON THE CONSISTENCY OF THE CONSTRAINT ALGEBRA IN SPIN NETWORK QUANTUM GRAVITY
GAMBINI, R., LEWANDOWSKI, J., MAROLF, D., & PULLIN, J. (1998) · International Journal of Modern Physics D · doi:10.1142/s0218271898000103 · Cited by 77 · see citing works
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- [9]R. Gambini, J. Pullin 'Loops, knots, gauge theories and quantum gravity' Cambridge University Press (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
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
- Bartolo, C. D., Gambini, R., Griego, J., & Pullin, J.
- Affiliations
- Universidad Simón Bolívar (VE)
- Pennsylvania State University (US)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2000-08-02
- Volume
- 17
- Issue
- 16
- Pages
- 3239-3264
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W1997717507
- Cited by
- 21
- References
- 6
- Citations by year
- 2013: 2
- FWCI
- 2.94
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Civil War Book Review (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, constraint algebra
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