Knot invariants as nondegenerate quantum geometries
Abstract
The loop-space representation based on Ashtekar's new variables has allowed for the first time the construction of quantum states of the gravitational field. However, all states known up to the present were associated with spacetime metrics that were everywhere degenerate. In this Letter we present a new exact solution of the constraint equations of quantum gravity that is the first quantum state of the gravitational field known to be associated with a not-everywhere-degenerate metric. The state is associated with the second coefficient of the Alexander-Conway polynomial of knot theory.
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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
New Hamiltonian formulation of general relativity
Ashtekar, A. (1987) · Physical Review D · doi:10.1103/physrevd.36.1587 · Cited by 1,119 · see citing works
Loop space representation of quantum general relativity
Rovelli, C., & Smolin, L. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90019-a · Cited by 806 · see citing works
Exact equation for the loop average in multicolor QCD
Makeenko, Y. M., & Migdal, A. (1979) · Physics Letters B · doi:10.1016/0370-2693(79)90131-x · Cited by 468 · 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
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
Gauge dynamics in the C-representation
Gambini, R., & Trias, A. (1986) · Nuclear Physics B · doi:10.1016/0550-3213(86)90221-x · Cited by 130 · see citing works
Self-citationBianchi cosmologies: the role of spatial topology
Ashtekar, A., & Samuel, J. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/12/005 · Cited by 124 · see citing works
Ashtekar, A., Carlo Rovelli, C., & Smolin, L. (1991) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.44.1740 · Cited by 96 · see citing works
Geometrical 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-citationProperties of the loop average in QCD
Migdal, A. (1980) · Annals of Physics · doi:10.1016/0003-4916(80)90177-3 · Cited by 80 · see citing works
Loop 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-citationGeneral covariance, new variables, and dynamics without dynamics
Husain, V., & Kuchař, K. V. (1990) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.42.4070 · Cited by 77 · see citing works
Second 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-citationLoop calculus for lattice gauge theories
Gambini, R., Leal, L., & Trias, A. (1989) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.39.3127 · Cited by 48 · see citing works
Self-citationIntersecting-loop solutions of the hamiltonian constraint of quantum general relativity
Husain, V. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90403-3 · Cited by 40 · 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-citationChiral formulation of Yang-Mills equations: A geometric approach
Gambini, R., & Trias, A. (1983) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.27.2935 · Cited by 27 · see citing works
Self-citationHusain, V. (1991) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.43.1803 · Cited by 24 · see citing works
Abelian Chern-Simons theory and CFT of rational torus
Li, M. (1990) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02827320 · Cited by 8 · see citing works
Fourier transforms on 𝒜/𝒢 and knot invariants
Majid, S. (1990) · Journal of Mathematical Physics · doi:10.1063/1.529026 · Cited by 6 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
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
(1998) · doi:10.12942/lrr-1998-1 · Cited by 917 · see citing works
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/011 · Cited by 750 · see citing works
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
“Sum over surfaces” form of loop quantum gravity
Reisenberger, M. P., & Rovelli, C. (1997) · Physical Review D · doi:10.1103/physrevd.56.3490 · Cited by 372 · see citing works
Loop quantum gravity and light propagation
Alfaro, J., Morales-Técotl, H. A., & Urrutia, L. F. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.65.103509 · Cited by 337 · see citing works
Carlo Rovelli, C. (2006) · The frontiers collection · doi:10.1007/978-3-319-55420-4_10 · Cited by 347 · see citing works
Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
Thiemann, T. (1996) · Physics Letters B · doi:10.1016/0370-2693(96)00532-1 · Cited by 284 · see citing works
Quantum spin dynamics (QSD): II. The kernel of the Wheeler - DeWitt constraint operator
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/012 · Cited by 247 · see citing works
Linking topological quantum field theory and nonperturbative quantum gravity
Smolin, L. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531251 · Cited by 234 · see citing works
Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
Thiemann, T. (1996) · Cited by 228 · see citing works
Actions for gravity, with generalizations: a title
Peldán, P. (1994) · Classical and Quantum Gravity · doi:10.1088/0264-9381/11/5/003 · Cited by 216 · 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
Loop Quantum Gravity: An Inside View
Thiemann, T. (2007) · Lecture notes in physics · doi:10.1007/978-3-540-71117-9_10 · Cited by 137 · see citing works
Link invariants of finite type and perturbation theory
Baez, J. C. (1992) · Letters in Mathematical Physics · doi:10.1007/bf00420517 · Cited by 116 · see citing works
Quantum gravity and spin-1/2 particle effective dynamics
Alfaro, J., Morales-Técotl, H. A., & Urrutia, L. F. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.124006 · Cited by 114 · see citing works
The dynamical structure of higher dimensional Chern-Simons theory
Bañados, M., Garay, L. J., & Marc Henneaux, A. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00384-7 · Cited by 117 · see citing works
Clock and category: is quantum gravity algebraic?
Crane, L. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 106 · see citing works
Clock and category: Is quantum gravity algebraic?
Crane, L. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531240 · Cited by 102 · see citing works
Loop quantum gravity: the first 25 years
Carlo Rovelli, C. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/15/153002 · Cited by 92 · see citing works
The dynamical structure of higher dimensional Chern-Simons theory
Máximo Bañados, A., Garay, L. J., & Marc Henneaux, A. (1996) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · Cited by 80 · see citing works
Holographic formulation of quantum general relativity
Smolin, L. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.084007 · Cited by 59 · see citing works
Matrix elements of Thiemann's Hamiltonian constraint in loop quantum gravity
Borissov, R., Pietri, R. D., & Carlo Rovelli, C. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/10/008 · Cited by 59 · see citing works
Aspects of canonical gravity and supergravity
Nicolai, H., & Matschull, H.-J. (1993) · Journal of Geometry and Physics · doi:10.1016/0393-0440(93)90047-i · Cited by 51 · see citing works
Quantum gravity: A brief history of ideas and some prospects
Carlip, S., Chiou, D.-W., Ni, W.-T., & Woodard, R. (2015) · International Journal of Modern Physics D · doi:10.1142/s0218271815300281 · Cited by 47 · see citing works
How the Jones polynomial gives rise to physical states of quantum general relativity
Brügmann, B., Gambini, R., & Pullin, J. (1993) · General Relativity and Gravitation · doi:10.1007/bf00756923 · Cited by 40 · see citing works
Self-citationOn the constraints of quantum gravity in the loop representation
Brügmann, B., & Pullin, J. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90462-x · Cited by 40 · see citing works
Self-citationChiou, D.-W. (2014) · International Journal of Modern Physics D · doi:10.1142/s0218271815300050 · Cited by 39 · see citing works
Moduli-space structure of knots with intersections
Grot, N., & Carlo Rovelli, C. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531527 · Cited by 38 · see citing works
Group of loops, holonomy maps, path bundle and path connection
Lewandowski, J. (1993) · Classical and Quantum Gravity · doi:10.1088/0264-9381/10/5/008 · Cited by 37 · see citing works
The extended loop group: An infinite dimensional manifold associated with the loop space
Bartolo, C. D., Gambini, R., & Griego, J. (1993) · Communications in Mathematical Physics · doi:10.1007/bf02108073 · Cited by 35 · see citing works
Self-citationGoldberg, J. N., Lewandowski, J., & Stornaiolo, C. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02100867 · Cited by 34 · see citing works
Extended loop representation of quantum gravity
Bartolo, C. D., Gambini, R., & Griego, J. (1995) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.51.502 · Cited by 30 · see citing works
Self-citationCarlo Rovelli, C. (2006) · AIP conference proceedings · doi:10.1063/1.2399564 · Cited by 29 · see citing works
Eleven-dimensional supergravity as a constrained topological field theory
Ling, Y., & Smolin, L. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00063-3 · Cited by 29 · see citing works
Finite diffeomorphism-invariant observables in quantum gravity
Smolin, L. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.4028 · Cited by 26 · see citing works
Knots and Quantum Gravity: Progress and ProspectsPreprint
Baez, J. C. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9410018 · Cited by 27 · see citing works
Quantum gravity as a Fermi liquidPreprint
Alexander, S., & Calcagni, G. (2016) · Cited by 25 · see citing works
On loop states in quantum gravity and supergravity
Matschull, H.-J. (1994) · Classical and Quantum Gravity · doi:10.1088/0264-9381/11/10/002 · Cited by 24 · see citing works
Extended loops: A new arena for nonperturbative quantum gravity
Bartolo, C. D., Gambini, R., Griego, J., & Pullin, J. A. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.3638 · Cited by 24 · see citing works
Self-citationBrügmann, B. (2008) · Springer eBooks · doi:10.1007/3-540-58339-4_20 · Cited by 23 · see citing works
Self-citationQuantum gravity: A brief history of ideas and some prospects
Carlip, S., Chiou, D.-W., Ni, W.-T., & Woodard, R. (2015) · eScholarship (California Digital Library) · Cited by 23 · see citing works
Lattice knot theory and quantum gravity in the loop representation
Fort, H., Gambini, R., & Pullin, J. (1997) · Physical Review D · doi:10.1103/physrevd.56.2127 · Cited by 22 · see citing works
Self-citationSuperconducting loop quantum gravity and the cosmological constant
Alexander, S., & Calcagni, G. (2009) · Physics Letters B · doi:10.1016/j.physletb.2009.01.046 · Cited by 22 · see citing works
Quantum Gravity as a Fermi Liquid
Alexander, S., & Calcagni, G. (2008) · Foundations of Physics · doi:10.1007/s10701-008-9257-6 · Cited by 22 · see citing works
Ψ=We ±Φ Quantum cosmological solutions for class A Bianchi models
Obregón, O., & Socorro, J. (1996) · International Journal of Theoretical Physics · doi:10.1007/bf02084947 · Cited by 22 · see citing works
Bartolo, C. D., Gambini, R., Griego, J., & Pullin, J. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/16/310 · Cited by 21 · see citing works
Self-citationReal alternative to quantum gravity in loop space
Loll, R. (1996) · Physical Review D · doi:10.1103/physrevd.54.5381 · Cited by 19 · see citing works
Quantum Gravity and the algebra of tanglesPreprint
Baez, J. C. (1992) · Cited by 19 · see citing works
Ashtekar, A. (2008) · Springer eBooks · doi:10.1007/3-540-58339-4_24 · Cited by 18 · see citing works
Knot polynomial states of quantum gravity in terms of loops and extended loops: Some remarks
Bartolo, C. D., Gambini, R., Griego, J., & Pullin, J. A. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531254 · Cited by 18 · see citing works
Self-citationIs the third coefficient of the Jones knot polynomial a quantum state of gravity?
Griego, J. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.53.6966 · Cited by 18 · see citing works
Quantum loop representation for fermions coupled to an Einstein-Maxwell field
Krasnov, K. V. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.53.1874 · Cited by 17 · see citing works
Rigorous solution of the quantum Einstein equations
Gambini, R., & Pullin, J. A. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.54.r5935 · Cited by 17 · see citing works
Self-citationCovariant quantization of membrane dynamics
Smolin, L. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.6216 · Cited by 16 · see citing works
Candidate for a background independent formulation of M theory
Smolin, L. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.62.086001 · Cited by 18 · see citing works
Quantum Einstein-Maxwell fields: A unified viewpoint from the loop representation
Gambini, R., & Pullin, J. A. (1993) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.47.r5214 · Cited by 13 · see citing works
Self-citationLoop Quantum Gravity and planck Scale Phenomenology
Smolin, L. (2005) · Springer eBooks · doi:10.1007/11377306_11 · Cited by 12 · see citing works
On the constraint algebra of quantum gravity in the loop representation
Brügmann, B. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00241-6 · Cited by 11 · see citing works
Self-citationChromodynamics and Gravity as Theories on Loop SpacePreprint
Loll, R. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9309056 · Cited by 11 · see citing works
The Kauffman bracket and the Jones polynomial in quantum gravity
Griego, J. R. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 11 · see citing works
Knot theory and the dynamics of quantum general relativity
Gambini, R., & Pullin, J. A. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/11/001 · Cited by 9 · see citing works
Self-citationThe Kauffman bracket and the Jones polynomial in quantum gravity
Griego, J. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00106-x · Cited by 9 · see citing works
An analytical expression for the third coefficient of the Jones polynomial
Bartolo, C. D., & Griego, J. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91369-x · Cited by 8 · see citing works
Polymer Geometry at Planck Scale and Quantum Einstein Equations
Ashtekar, A. (1996) · Springer eBooks · doi:10.1007/978-94-009-0237-4_12 · Cited by 10 · see citing works
Open-flux solutions to the quantum constraints for plane gravity waves
Neville, D. E. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.55.766 · Cited by 8 · see citing works
Bruegmann, B. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9303015 · Cited by 8 · see citing works
Energy and directional signatures for plane quantized gravity waves
Neville, D. E. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.57.986 · Cited by 7 · see citing works
Witten's identity for Chern-Simons theory
Br�gmann, B. (1995) · International Journal of Theoretical Physics · doi:10.1007/bf00672798 · Cited by 7 · see citing works
Self-citationSchilling, T. A. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9409031 · Cited by 7 · see citing works
Extended knots and the space of states of quantum gravity
Griego, J. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00235-0 · Cited by 7 · see citing works
Precision Measurements of the W Boson Mass
Glenzinskí, D., & Heintz, U. (2000) · Annual Review of Nuclear and Particle Science · doi:10.1146/annurev.nucl.50.1.207 · Cited by 6 · see citing works
Quantum gravity and the algebra of tangles
Baez, J. C. (1993) · Classical and Quantum Gravity · doi:10.1088/0264-9381/10/4/006 · Cited by 6 · see citing works
Beetle, C., & Corichi, A. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9703044 · Cited by 6 · see citing works
Link invariants for intersecting loops
Armand-Ugon, D., Gambini, R., & Mora, P. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)90110-4 · Cited by 6 · see citing works
Self-citationSpin Networks, Topology and Discrete Physics
Kauffman, L. H. (1994) · Advanced series in mathematical physics · doi:10.1142/9789812798275_0009 · Cited by 6 · see citing works
A spin network generalization of the Jones polynomial and Vassiliev invariants
Gambini, R., Griego, J., & Pullin, J. (1998) · Physics Letters B · doi:10.1016/s0370-2693(98)00182-8 · Cited by 5 · see citing works
Self-citationA spin network generalization of the Jones polynomial and Vassiliev invariants
Gambini, R., Griego, J., & Pullin, J. A. (1998) · Civil War Book Review · Cited by 5 · see citing works
Self-citationInteracting Euclidean three-dimensional quantum gravity
Bonacina, G., Gamba, A., & Martellini, M. (1992) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.45.3577 · Cited by 4 · see citing works
Does loop quantum gravity imply Λ=0?
Gambini, R., & Pullin, J. A. (1998) · Physics Letters B · doi:10.1016/s0370-2693(98)00915-0 · Cited by 3 · see citing works
Self-citationDegenerate triads and reality conditions in canonical gravity
Maluf, J. W. (1993) · Classical and Quantum Gravity · doi:10.1088/0264-9381/10/4/016 · Cited by 3 · see citing works
Classical loop actions of gauge theories
Armand-Ugon, D., Gambini, R., Griego, J., & Setaro, L. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.50.5352 · Cited by 3 · see citing works
Self-citationComplete quantization of a diffeomorphism invariant field theory
Thiemann, T. (1995) · Classical and Quantum Gravity · doi:10.1088/0264-9381/12/1/006 · Cited by 3 · see citing works
Graph Invariants of Vassiliev Type and Application to 4D Quantum GravityPreprint
Hayashi, N. (1996) · Cited by 3 · see citing works
The ADM papers and part of their modern legacy: loop quantum gravity
Pullin, J. A. (2015) · Classical and Quantum Gravity · doi:10.1088/0264-9381/32/12/124004 · Cited by 1 · see citing works
Self-citationThe ADM papers and part of their modern legacy: Loop quantum gravity
Pullin, J. A. (2015) · Civil War Book Review · Cited by 1 · see citing works
Self-citationVassiliev Invariants and the Loop States in Quantum GravityPreprint
Kauffman, L. H. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9310035 · Cited by 1 · see citing works
Graph invariants of Vassiliev type and application to 4D quantum gravity
Hayashi, N. (1996) · Communications in Mathematical Physics · doi:10.1007/bf02099627 · Cited by 1 · see citing works
Complete quantization of a diffeomorphism invariant field theoryPreprint
Thiemann, T. (1995) · Cited by 1 · see citing works
Loop Variables in Quantum Gravity and Vassiliev Invariants
Picken, R. (1994) · Springer eBooks · doi:10.1007/978-1-4615-2564-6_4
Generalized coordinates on the phase space of Yang-Mills theory
Loll, R., Mourão, J. M., & Tavares, J. N. (1995) · Classical and Quantum Gravity · doi:10.1088/0264-9381/12/5/010
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Alexander, S. (2016) · International Journal of Theoretical Physics · doi:10.1007/s10773-016-3169-6
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Faraji, S. (2026) · Fortschritte der Physik · doi:10.1002/prop.70156
Baez, J. C. (1993) · arXiv · doi:10.48550/arxiv.hep-th/9305045 · Cited by 78 · see citing works
- Authors
- Brügmann, B., Gambini, R., & Pullin, J.
- Affiliations
- Universidad de la República de Uruguay (UY)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1992-01-27
- Volume
- 68
- Issue
- 4
- Pages
- 431-434
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W1972512086
- Cited by
- 94
- References
- 24
- Citations by year
- 2026: 1 · 2016: 2 · 2015: 4 · 2014: 1
- FWCI
- 10.94
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Civil War Book Review (submittedVersion)
- 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
- knot invariants, quantum gravity, Ashtekar variables, loop quantum gravity, degenerate metrics, constraint equations, Alexander-Conway polynomial, exact solutions
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