How the Jones polynomial gives rise to physical states of quantum general relativity
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The scalar product defined in this way is precisely the one defined on the loop representation by the loop transform of the Ashtekar-Lewandowski measure, namely the conventional Haar measure lattice gauge theory scalar product for each graph.
“We think that the scalar product defined in this way is precisely the one defined on the loop representation by the loop transform [3,4] of the Ashtekar-Lewandowski measure [53], namely the conventional Haar measure lattice gauge theory scalar product for each graph.”
From Geometry eigenvalues and the scalar product from recoupling theory in loop quantum gravity (1996) · cites this paper as [53]
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Cites
Quantum field theory and the Jones polynomial
Witten, E. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01217730 · Cited by 4,758 · see citing works
New Variables for Classical and Quantum Gravity
Ashtekar, A. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.2244 · Cited by 1,663 · see citing works
Knot Theory and Quantum Gravity
Rovelli, C., & Smolin, L. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.1155 · Cited by 463 · see citing works
Nonperturbative quantum geometries
Jacobson, T., & Smolin, L. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90286-6 · Cited by 283 · see citing works
Wilson lines in Chern-Simons theory and link invariants
Guadagnini, E., Martellini, M., & Mintchev, M. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90124-v · Cited by 252 · see citing works
Holomorphic wave function of the Universe
Kodama, H. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.2548 · Cited by 232 · see citing works
2+1 quantum gravity as a toy model for the 3+1 theory
Ashtekar, A., Husain, V, Rovelli, C., Samuel, J., & Smolin, L. (1989) · Classical and Quantum Gravity · doi:10.1088/0264-9381/6/10/001 · Cited by 165 · see citing works
Jones polynomials for intersecting knots as physical states of quantum gravity
Brügmann, B., Gambini, R., & Pullin, J. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90060-o · Cited by 98 · see citing works
Self-citationKnot 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-citationGeometrical origin of gauge theories
Gambini, R., & Trias, A. (1981) · Physical Review D · doi:10.1103/physrevd.23.553 · Cited by 94 · see citing works
Self-citationLoop space representation of quantum general relativity and the group of loops
Gambini, R. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)90233-g · Cited by 78 · see citing works
Self-citationSecond quantization of the free electromagnetic field as quantum mechanics in the loop space
Gambini, R., & Trias, A. (1980) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.22.1380 · Cited by 70 · see citing works
Self-citationIntersecting N loop solutions of the hamiltonian constraint of quantum gravity
Brügmann, B., & Pullin, J. A. (1991) · Nuclear Physics B · doi:10.1016/0550-3213(91)90242-p · Cited by 53 · see citing works
Self-citationA Loop Representation for the Quantum Maxwell Field
Ashtekar, A., & Carlo Rovelli, C. (1992) · CERN Document Server (European Organization for Nuclear Research) · Cited by 38 · see citing works
Method of loops applied to lattice gauge theory
Brügmann, B. (1991) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.43.566 · Cited by 32 · see citing works
Self-citationKnot invariants as nondegenerate states of four-dimensional quantum gravity
Gambini, R., Bruegmann, B., & Pullin, J. A. (1991) · Cited by 11 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 4
- [3][3] C. Di Bartolo, R. Gambini, J. Griego, L. Leal, Preprint IFFI (1991) (Montevideo). -
- [7][7] B. Br¨ ugmann, J. Pullin, Syracuse University Preprint SU-GP-91/8-5 (1991). -
- [12][12] A. Ashtekar, C. Rovelli, Syracuse University Preprint (1991). -
- [16][16] R. A. Farrerons, Ph. D. Thesis, Universitat Aut` onoma de Barcelona (1990). -
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Sorted by citations
Spin networks and quantum gravity
Rovelli, C., & Smolin, L. (1995) · Physical Review D · doi:10.1103/physrevd.52.5743 · Cited by 629 · see citing works
Geometry eigenvalues and the scalar product from recoupling theory in loop quantum gravity
De Pietri, R., & Rovelli, C. (1996) · Physical Review D · doi:10.1103/physrevd.54.2664 · Cited by 201 · see citing works
- Authors
- Brügmann, B., Gambini, R., & Pullin, J.
- Affiliations
- Syracuse University (US)
- Universidad de la República de Uruguay (UY)
- University of Utah (US)
- Venue
- General Relativity and Gravitation
- Published
- 1993-01
- Volume
- 25
- Issue
- 1
- Pages
- 1-6
- ISSN
- 0001-7701 (ISSN-L)
- 1572-9532
- OpenAlex
- W2075198574
- Cited by
- 40
- References
- 16
- Citations by year
- 2016: 1 · 2012: 1
- FWCI
- 5.65
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- General Relativity and Gravitation (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Civil War Book Review (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Syracuse University
- Comisión Nacional de Investigación Científica y Tecnológica
- 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
- Jones polynomial, quantum gravity, loop representation, Ashtekar variables, diffeomorphism constraint, Hamiltonian constraint, knot invariants, knot theory, solution space
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