On relativistic spin network vertices
Open accessAbstract
Barrett and Crane have proposed a model of simplicial Euclidean quantum gravity in which a central role is played by a class of Spin(4) spin networks called “relativistic spin networks” which satisfy a series of physically motivated constraints. Here a proof is presented that demonstrates that the intertwiner of a vertex of such a spin network is uniquely determined, up to normalization, by the representations on the incident edges and the constraints. Moreover, the constraints, which were formulated for four valent spin networks only, are extended to networks of arbitrary valence, and the generalized relativistic spin networks proposed by Yetter are shown to form the entire solution set (mod normalization) of the extended constraints. Finally, using the extended constraints, the Barrett–Crane model is generalized to arbitrary polyhedral complexes (instead of just simplicial complexes) representing space-time. It is explained how this model, like the Barret–Crane model can be derived from BF theory, a simple topological field theory [G. Horowitz, Commun. Math. Phys. 125, 417 (1989)], by restricting the sum over histories to ones in which the left-handed and right-handed areas of any 2-surface are equal. It is known that the solutions of classical Euclidean general relativity form a branch of the stationary points of the BF action with respect to variations preserving this condition.
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The state space of strong solutions of the quadratic quantum Plebanski constraints is one-dimensional and given by the Barrett-Crane intertwiner.
“Indeed, it has been shown that the state space of strong solutions of the quadratic quantum Plebanski constraints is one dimensional and it is given by the BC intertwiner |BC⟩ [313].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [313]
The EPRL and Freidel-Krasnov derivations produced a new, consistent spin-foam model valid for the Barbero-Immirzi parameter in the interval -1 ≤ γ ≤ 1.
“The result of their effort is a new, consistent spin-foam model valid for the Barbero-Immirzi parameter belonging to the interval -1 ≤ γ ≤ 1, a promising candidate for a path integral formulation of LQG, and two different models for | γ | > 1 [14-16]”
From Spin-foams for all loop quantum gravity (2010) · cites this paper as [16]
There are two different spin-foam models for |γ| > 1.
“The result of their effort is a new, consistent spin-foam model valid for the Barbero-Immirzi parameter belonging to the interval -1 ≤ γ ≤ 1, a promising candidate for a path integral formulation of LQG, and two different models for | γ | > 1 [14-16]”
From Spin-foams for all loop quantum gravity (2010) · cites this paper as [16]
Under suitable conditions, a fat graph can be put in correspondence with a four-dimensional triangulated manifold, so the sum over Feynman graphs is a sum over triangulations.
“In fact, under suitable conditions [92,93], a fat graph can be put in correspondence with a four-dimensional triangulated manifold, so that the sum over Feynman graphs is a sum over triangulations.”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [93]
Fat graphs representing Feynman diagrams are in direct correspondence with 2-complexes, which can be interpreted as the dual 2-skeleton of a triangulation.
“More precisely [92,93], the fat graphs representing Feynman diagrams of our field theory are in direct correspondence with 2-complexes, as we have seen, that can in turn be interpreted as the dual 2-skeleton of a triangulation”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [93]
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Cites
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 theory of geometry: I. Area operators
Ashtekar, A., & Lewandowski, J. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1a/006 · Cited by 852 · 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
Quantum theory of geometry II: Volume operators
Ashtekar, A., & Lewandowski, J. (1997) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1997.v1.n2.a8 · Cited by 580 · see citing works
Relativistic Spin Networks and Quantum GravityPreprint
Barrett, J. W., Crane, L., & Crane, J. W. B. L. (1998) · Cited by 423 · see citing works
Relativistic spin networks and quantum gravity
Barrett, J. W., & Crane, L. (1998) · Journal of Mathematical Physics · doi:10.1063/1.532254 · Cited by 404 · see citing works
TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS
OOGURI, H. (1992) · Modern Physics Letters A · doi:10.1142/s0217732392004171 · Cited by 379 · see citing works
Mathematical apparatus of the theory of angular momentum
institutas, F. I. M., I︠U︡t︠s︡is, A. P., Levinson, I. B., & Vanagas, V. V. (1962) · Israel Program for Scientific Translations eBooks · Cited by 302 · see citing works
Baez, J. C. (1996) · Advances in Mathematics · doi:10.1006/aima.1996.0012 · Cited by 266 · 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
State sum invariants of 4-manifolds
Crane, L., Kauffman, L. H., & Yetter, D. N. (1997) · Journal of Knot Theory and Its Ramifications · doi:10.1142/s0218216597000145 · Cited by 139 · see citing works
Quantum tetrahedra and simplicial spin networks
Barbieri, A. (1998) · Nuclear Physics B · doi:10.1016/s0550-3213(98)00093-5 · Cited by 113 · see citing works
Quantum tetrahedra and simplicial spin networks
Barbieri, A. (1997) · CERN Document Server (European Organization for Nuclear Research) · Cited by 99 · see citing works
The complete spectrum of the area from recoupling theory in loop quantum gravity
Frittelli, S., Lehner, L., & Rovelli, C. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/11/008 · Cited by 95 · see citing works
Classical Euclidean general relativity from `left-handed area = right-handed area'
Reisenberger, M. P. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/4/024 · Cited by 94 · see citing works
Self-citationSymmetrical Coupling of Three Angular Momenta
Lévy-Leblond, J.-M., & Nahas, M. (1965) · Journal of Mathematical Physics · doi:10.1063/1.1704786 · Cited by 83 · see citing works
The complete spectrum of the area from recoupling theory in loop quantum gravity
Frittelli, S., Lehner, L., & Carlo Rovelli, C. (1996) · CERN Document Server (European Organization for Nuclear Research) · Cited by 82 · see citing works
A left-handed simplicial action for Euclidean general relativity
Reisenberger, M. P. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/7/012 · Cited by 73 · see citing works
Self-citationA lattice worldsheet sum for 4-d Euclidean general relativityPreprint
Reisenberger, M. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9711052 · Cited by 73 · see citing works
Self-citationThe classical evaluation of relativistic spin networks
Barrett, J. W. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n3.a7 · Cited by 60 · see citing works
Worldsheet formulations of gauge theories and gravityPreprint
Reisenberger, M. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9412035 · Cited by 60 · see citing works
Self-citationGENERALIZED BARRETT–CRANE VERTICES AND INVARIANTS OF EMBEDDED GRAPHS
Yetter, D. N. (1999) · Journal of Knot Theory and Its Ramifications · doi:10.1142/s0218216599000511 · Cited by 23 · see citing works
Space of the vertices of relativistic spin networksPreprint
Barbieri, R. A. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9709076 · Cited by 7 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- [Pen69] R. Penrose. Angular momentum: an approach to combinatorial spacetime. In T. Bastin, editor, Quantum theory and beyond , 1969. Cambridge University Press.
Cited by
Sorted by citations
Background independent quantum gravity: a status report
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Spin foam models for quantum gravity
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New spinfoam vertex for quantum gravity
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Loop-Quantum-Gravity Vertex Amplitude
Engle, J., Pereira, R., & Rovelli, C. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.161301 · Cited by 335 · see citing works
A Lorentzian signature model for quantum general relativity
Barrett, J. W., & Crane, L. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/16/302 · Cited by 275 · see citing works
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Barrett–Crane model from a Boulatov–Ooguri field theory over a homogeneous space
De Pietri, R., Freidel, L., Krasnov, K., & Rovelli, C. (2000) · Nuclear Physics B · doi:10.1016/s0550-3213(00)00005-5 · Cited by 244 · see citing works
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
Barrett, J. W., Dowdall, R. J., Fairbairn, W. J., Hellmann, F., & Pereira, R. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/16/165009 · Cited by 247 · see citing works
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Engle, J., Pereira, R., & Rovelli, C. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.02.002 · Cited by 241 · see citing works
Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
Oriti, D. (2001) · Reports on Progress in Physics · doi:10.1088/0034-4885/64/12/203 · Cited by 201 · see citing works
Discrete Structures in Gravity
Regge, T., & Williams, R. M. (2000) · CERN Document Server (European Organization for Nuclear Research) · Cited by 182 · see citing works
Solving the simplicity constraints for spinfoam quantum gravity
Livine, E. R., & Simone Speziale, D. (2008) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/81/50004 · Cited by 180 · see citing works
Discrete structures in gravity
Regge, T., & Williams, R. M. (2000) · Journal of Mathematical Physics · doi:10.1063/1.533333 · Cited by 148 · see citing works
The Quantum Tetrahedron in 3 and 4 Dimensions
Baez, J. C., & Barrett, J. W. (1999) · arXiv · doi:10.48550/arxiv.gr-qc/9903060 · Cited by 146 · see citing works
The quantum tetrahedron in 3 and 4 dimensions
Baez, J. C., & Barrett, J. W. (1999) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1999.v3.n4.a3 · Cited by 146 · see citing works
Spin-foams for all loop quantum gravity
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Time evolution as refining, coarse graining and entangling
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Cosmological deformation of Lorentzian spin foam models
Noui, K., & Roche, P. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/14/318 · Cited by 71 · see citing works
Perturbative Finiteness in Spin-Foam Quantum Gravity
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Loop and Spin Foam Quantum Gravity: A Brief Guide for Beginners
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Alexandrov, S. Y. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.77.024009 · Cited by 55 · see citing works
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- Authors
- Reisenberger, M. P.
- Affiliations
- Universidad de la República de Uruguay (UY)
- Corresponding author
- Reisenberger, Michael P.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1999-04-01
- Volume
- 40
- Issue
- 4
- Pages
- 2046-2054
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2118522035
- Cited by
- 72
- References
- 23
- Citations by year
- 2025: 1 · 2024: 1 · 2023: 1 · 2022: 1 · 2016: 1 · 2015: 2 · 2014: 3 · 2013: 2 · 2012: 3
- FWCI
- 5.67
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (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
- Barrett-Crane model, polyhedral complexes, simplicial quantum gravity, BF theory, topological field theory
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