so (4) Plebanski action and relativistic spin-foam model
Open accessAbstract
We study the correspondence between the `relativistic spin-foam' model introduced by Barrett, Crane and Baez and the so (4) Plebanski action. We argue that the so (4) Plebanski model is the continuum analogue of the relativistic spin-foam model. We prove that the so (4) Plebanski action possesses four phases, one of which is related to gravity and discuss the relation between this model and the model of Euclidean tetrad gravity. We also show that the so (4) Plebanski model possesses another natural discretization that can be associated with another, new, spin-foam model which appear to be the so (4) counterpart of the spin-foam model describing the self-dual formulation of gravity.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Generalized matrix models probably offer a path to include matter, because coupling of matter fields to gravity was already studied in two-dimensional matrix models [109,115,116].
“The construction of the generalized matrix models gives probably a path to follow in this direction, since the coupling of matter fields to gravity was already studied in the context of two-dimensional matrix models [109,115,116].”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [109]
The second class constraints can be translated into simplicity constraints restricting the used SL(2,C) representations to simple ones, which have a vanishing quadratic Casimir operator.
“They can then be translated into the so-called simplicity constraints restricting the used SL (2 , C ) representations to simple ones, which have a vanishing quadratic Casimir operator [27, 25, 26].”
The Barrett-Crane model's construction relies on methods from geometrical quantization, but can also be related to the generalised Palatini action (with Immirzi parameter) through a generalised constrained BF theory.
“Its construction relies on methods from geometrical quantization [21, 23], but can also be related to the generalised Palatini action (with Immirzi parameter) through a generalised constrained BF theory [24, 25, 26].”
The spin foam quantization of the generalized Hilbert-Palatini action was shown not to depend on the Immirzi parameter.
“Similarly, the spin foam quantization, which can be understood as a discrete path integral, of the generalized Hilbert-Palatini action was shown not to depend on the Immirzi parameter [25, 26].”
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
On the separation of Einsteinian substructures
Plebański, J. F. (1977) · Journal of Mathematical Physics · doi:10.1063/1.523215 · Cited by 499 · 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
Baez, J. C. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/7/004 · Cited by 381 · 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
Capovilla, R., Dell, J., Jacobson, T., & Mason, L. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/1/009 · Cited by 286 · see citing works
Spin foam models and the classical action principle
Freidel, L., & Krasnov, K. (1998) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.1998.v2.n6.a1 · Cited by 195 · see citing works
Self-citationA pure spin-connection formulation of gravity
Capovilla, R., Dell, J., & Jacobson, T. (1991) · Classical and Quantum Gravity · doi:10.1088/0264-9381/8/1/010 · Cited by 162 · see citing works
On integrability properties of SU (2) Yang–Mills fields. I. Infinitesimal part
Urbantke, H. K. (1984) · Journal of Mathematical Physics · doi:10.1063/1.526402 · Cited by 96 · 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
A 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
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
A categorical construction of 4D TQFTsPreprint
Crane, L., & Yetter, D. N. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9301062 · Cited by 43 · see citing works
Discrete spacetime volume for three-dimensional BF theory and quantum gravity
Freidel, L., & Krasnov, K. V. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/2/003 · Cited by 41 · see citing works
Self-citationNew constraints for canonical general relativity
Reisenberger, M. P. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00448-3 · Cited by 36 · see citing works
New Constraints for Canonical General RelativityPreprint
Reisenberger, M. (1995) · Cited by 36 · see citing works
GENERALIZED 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
Vacuum Einstein equations in terms of curvature forms
Obukhov, Y. N., & Tertychniy, S. I. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/6/025 · Cited by 16 · see citing works
Self-dual 2-form formulation of gravity and classification of energy - momentum tensors
Pillin, M. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/8/020 · Cited by 1 · see citing works
Asymptotic distributions on super-Riemann surfaces
Grosche, C. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/9/001 · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Reisenberger M 1998 Classical Euclidean general relativity from 'lefthanded area = righthanded area' Preprint gr-qc/9804061 · arXiv
Cited by
Sorted by citations
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
Spin foam models for quantum gravity
Perez, A. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/6/202 · Cited by 532 · see citing works
A new spin foam model for 4D gravity
Freidel, L., & Krasnov, K. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/12/125018 · Cited by 521 · see citing works
Self-citationQuantum gravity: a progress report
Carlip, S. (2001) · Reports on Progress in Physics · doi:10.1088/0034-4885/64/8/301 · Cited by 449 · see citing works
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
Group Field Theory: An Overview
Freidel, L. (2005) · International Journal of Theoretical Physics · doi:10.1007/s10773-005-8894-1 · Cited by 378 · see citing works
Self-citationGroup Field Theory: An overview
Freidel, L. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 249 · see citing works
Self-citationBarrett–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
Self-citationFlipped spinfoam vertex and loop gravity
Engle, J., Pereira, R., & Rovelli, C. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2008.02.002 · Cited by 241 · see citing works
The microscopic dynamics of quantum space as a group field theory
Oriti, D. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9780511920998.012 · Cited by 222 · see citing works
Semiclassical limit of 4-dimensional spin foam models
Conrady, F., & Freidel, L. (2008) · Physical Review D · doi:10.1103/physrevd.78.104023 · Cited by 213 · see citing works
Self-citationSpacetime 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
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
Area–angle variables for general relativity
Dittrich, B., & Simone Speziale, D. (2008) · New Journal of Physics · doi:10.1088/1367-2630/10/8/083006 · Cited by 147 · see citing works
Alexandrov, S., & Livine, E. R. (2003) · Physical Review D · doi:10.1103/physrevd.67.044009 · Cited by 141 · see citing works
Phase space descriptions for simplicial 4D geometries
Dittrich, B., & Ryan, J. P. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/6/065006 · Cited by 140 · see citing works
BF 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
Self-citationGroup field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity
Baratin, A., & Oriti, D. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.85.044003 · Cited by 136 · see citing works
Edge modes of gravity. Part II. Corner metric and Lorentz charges
Freidel, L., Geiller, M., & Pranzetti, D. (2020) · Journal of High Energy Physics · doi:10.1007/jhep11(2020)027 · Cited by 136 · see citing works
Self-citationAsymptotics of 6 <i>j</i> and 10 <i>j</i> symbols
Freidel, L., & Louapre, D. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/7/303 · Cited by 113 · see citing works
Self-citationEmergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
Oriti, D., Sindoni, L., & Wilson-Ewing, E. (2016) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/22/224001 · Cited by 112 · see citing works
Emergent Friedmann dynamics with a quantum bounce from quantum gravity condensates
Oriti, D., Sindoni, L., & Wilson-Ewing, E. (2016) · MPG.PuRe (Max Planck Society) · Cited by 110 · see citing works
Edge modes of gravity. Part III. Corner simplicity constraints
Freidel, L., Geiller, M., & Pranzetti, D. (2021) · Journal of High Energy Physics · doi:10.1007/jhep01(2021)100 · Cited by 109 · see citing works
Self-citationQuantum gravity in terms of topological observablesPreprint
Freidel, L., & Starodubtsev, A. N. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0501191 · Cited by 132 · see citing works
Self-citationSpin foam models for quantum gravity from lattice path integrals
Bonzom, V. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.064028 · Cited by 100 · see citing works
4-dimensional spin-foam model with quantum Lorentz group
Han, M. (2011) · Journal of Mathematical Physics · doi:10.1063/1.3606592 · Cited by 98 · see citing works
Hamiltonian analysis of Plebanski theory
Buffenoir, E., Marc Henneaux, A., Noui, K., & Roche, P. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/22/012 · Cited by 95 · see citing works
Quantum geometry from phase space reduction
Conrady, F., & Freidel, L. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3257109 · Cited by 97 · see citing works
Self-citationAsymptotics of spinfoam amplitude on simplicial manifold: Lorentzian theory
Han, M., & Zhang, M. (2013) · Classical and Quantum Gravity · doi:10.1088/0264-9381/30/16/165012 · Cited by 94 · see citing works
Baratin, A., & Oriti, D. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/12/125011 · Cited by 91 · see citing works
Spin Foams and Canonical Quantization
Alexandrov, S. Y. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.055 · Cited by 93 · see citing works
Simplicity in simplicial phase space
Dittrich, B., & Ryan, J. P. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.064026 · Cited by 81 · see citing works
Asymptotics of the spin foam amplitude on simplicial manifold: Euclidean theory
Han, M., & Zhang, M. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/16/165004 · Cited by 80 · see citing works
Projected spin networks for Lorentz connection: linking spin foams and loop gravity
Livine, E. R. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/21/316 · Cited by 77 · see citing works
Lorentzian loop quantum gravity vertex amplitude
Roberto Pereira, B. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/8/085013 · Cited by 77 · see citing works
Holomorphic simplicity constraints for 4D spinfoam models
Dupuis, M., & Livine, E. R. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/21/215022 · Cited by 75 · see citing works
Projected Spin Networks for Lorentz connection: Linking Spin Foams and Loop GravityPreprint
Livine, E. R. (2002) · Cited by 74 · see citing works
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
Holomorphic Lorentzian simplicity constraints
Dupuis, M., Freidel, L., Livine, E. R., & Speziale, S. (2012) · Journal of Mathematical Physics · doi:10.1063/1.3692327 · Cited by 64 · see citing works
Self-citationRegularization and finiteness of the Lorentzian loop quantum gravity vertices
Engle, J., & Pereira, R. (2009) · Physical Review D · doi:10.1103/physrevd.79.084034 · Cited by 63 · see citing works
Gravity and unification: a review
Krasnov, K., & Roberto Percacci, A. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aac58d · Cited by 59 · see citing works
Ding, Y., Han, M., & Rovelli, C. (2011) · Physical Review D · doi:10.1103/physrevd.83.124020 · Cited by 60 · 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
BF gravity and the Immirzi parameter
Capovilla, R., Montesinos, M., Prieto, V. A., & Rojas, E. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/5/101 · Cited by 55 · see citing works
Spin foam model from canonical quantization
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
Plebanski action extended to a unification of gravity and Yang-Mills theory
Smolin, L. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.80.124017 · Cited by 55 · see citing works
Group Field Theory Condensate Cosmology: An Appetizer
Pithis, A. G. A., & Sakellariadou, M. (2019) · Universe · doi:10.3390/universe5060147 · Cited by 54 · see citing works
Gluing 4-simplices: A derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity
Oriti, D., & Williams, R. M. (2000) · Physical Review D · doi:10.1103/physrevd.63.024022 · Cited by 54 · see citing works
A note on area variables in Regge calculusPreprint
Barrett, J. W., Martin Roček, B., Williams, R. M., & Ams-tex, T. (1997) · Cited by 54 · see citing works
Observables in loop quantum gravity with a cosmological constant
Dupuis, M., & Girelli, F. (2014) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.90.104037 · Cited by 56 · see citing works
Implementing causality in the spin foam quantum geometry
Livine, E. R., & Oriti, D. (2003) · Nuclear Physics B · doi:10.1016/s0550-3213(03)00378-x · Cited by 53 · see citing works
The century of the incomplete revolution: Searching for general relativistic quantum field theory
Carlo Rovelli, C. (2000) · Journal of Mathematical Physics · doi:10.1063/1.533327 · Cited by 53 · see citing works
Simplicity and closure constraints in spin foam models of gravity
Alexandrov, S. Y. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.044033 · Cited by 50 · see citing works
Celada, M., González, D., & Montesinos, M. (2016) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/21/213001 · Cited by 51 · see citing works
Spin foam model for pure gauge theory coupled to quantum gravity
Oriti, D., & Pfeiffer, H. (2002) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.66.124010 · Cited by 49 · see citing works
From lattice BF gauge theory to area–angle Regge calculus
Bonzom, V. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/15/155020 · Cited by 47 · see citing works
Proposed proper Engle-Pereira-Rovelli-Livine vertex amplitude
Engle, J. (2013) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.87.084048 · Cited by 47 · see citing works
Livine, R. E., & Oriti, D. (2002) · Physical Review D · doi:10.1103/physrevd.65.044025 · Cited by 46 · see citing works
Bimetric theory of gravity from the nonchiral Plebanski action
Simone Speziale, D. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.82.064003 · Cited by 45 · see citing works
BF gravity and the Immirzi parameter
Capovilla, R., Montesinos, M., PRIETO, V. A., & Rojas, E. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 43 · see citing works
Critical overview of loops and foams
Alexandrov, S. Y., & Roche, P. (2011) · Physics Reports · doi:10.1016/j.physrep.2011.05.002 · Cited by 42 · see citing works
Hamiltonian analysis of non-chiral Plebanski theory and its generalizations
Alexandrov, S. Y., & Krasnov, K. V. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/5/055005 · Cited by 41 · see citing works
A Immirzi-like parameter for 3D quantum gravity
Bonzom, V., & Livine, E. R. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/19/195024 · Cited by 41 · see citing works
Implementing causality in the spin foam quantum geometryPreprint
Livine, E. R., & Oriti, D. (2002) · Cited by 41 · see citing works
Unification of gravity, gauge fields and Higgs bosons
Lisi, A. G., Smolin, L., & Simone Speziale, D. (2010) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/43/44/445401 · Cited by 40 · see citing works
Revisiting the Simplicity Constraints and Coherent IntertwinersPreprint
Dupuis, M., & Livine, E. R. (2010) · HAL · Cited by 40 · see citing works
Causal structure and algebraic classification of non-dissipative linear optical media
Schuller, F. P., Witte, C., & Wohlfarth, M. N. R. (2010) · Annals of Physics · doi:10.1016/j.aop.2010.04.008 · Cited by 39 · see citing works
Lagrangian approach to the Barrett-Crane spin foam model
Bonzom, V., & Livine, E. R. (2009) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.79.064034 · Cited by 37 · see citing works
Asymptotic analysis of the EPRL model with timelike tetrahedra
Kamiński, W., Kisielowski, M., & Sahlmann, H. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aac6a4 · Cited by 37 · see citing works
Spin foam quantization of $SO(4)$ Plebanski’s action
Pérez, A. (2001) · Advances in Theoretical and Mathematical Physics · doi:10.4310/atmp.2001.v5.n5.a4 · Cited by 37 · see citing works
Chiral description of massive gravity
Alexandrov, S. Y., Krasnov, K. V., & Simone Speziale, D. (2013) · Journal of High Energy Physics · doi:10.1007/jhep06(2013)068 · Cited by 36 · see citing works
On the Relations between Gravity and BF Theories
Freidel, L. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.032 · Cited by 42 · see citing works
Self-citationClassical general relativity as BF-Plebanski theory with linear constraints
Gielen, S., & Oriti, D. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/18/185017 · Cited by 35 · see citing works
The perturbative Regge-calculus regime of loop quantum gravity
Bianchi, E., & Modesto, L. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2007.12.011 · Cited by 34 · see citing works
Covariant canonical formalism for four-dimensional BF theory
Mondragón, M., & Montesinos, M. (2006) · Journal of Mathematical Physics · doi:10.1063/1.2161805 · Cited by 34 · see citing works
Plebanski theory and covariant canonical formulation
Alexandrov, S. Y., Buffenoir, E., & Roche, P. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/11/003 · Cited by 34 · see citing works
GRAVITY AS BF THEORY PLUS POTENTIAL
Krasnov, K. V. (2009) · International Journal of Modern Physics A · doi:10.1142/s0217751x09046151 · Cited by 33 · see citing works
A new Hamiltonian for the topological BF phase with spinor networks
Bonzom, V., & Livine, E. R. (2012) · Journal of Mathematical Physics · doi:10.1063/1.4731771 · Cited by 35 · see citing works
Timelike surfaces in Lorentz covariant loop gravity and spin foam models
Alexandrov, S. Y., & Kádár, Z. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/17/010 · Cited by 29 · see citing works
Effective particle kinematics from quantum gravity
Kowalski-Glikman, J., & Starodubtsev, A. N. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.084039 · Cited by 25 · see citing works
Engle, J., Han, M., & Thiemann, T. (2010) · Cited by 27 · see citing works
Spin foam models and the Duflo map
Finocchiaro, M., & Oriti, D. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab58da · Cited by 25 · see citing works
Complete Barrett-Crane model and its causal structure
Jercher, A. F., Oriti, D., & Pithis, A. G. A. (2022) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.106.066019 · Cited by 25 · see citing works
Revisiting the simplicity constraints and coherent intertwiners
Dupuis, M., & Livine, E. R. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/8/085001 · Cited by 25 · see citing works
Towards effective actions for the continuum limit of spin foams
Borissova, J. N., & Dittrich, B. (2023) · Classical and Quantum Gravity · doi:10.1088/1361-6382/accbfb · Cited by 23 · see citing works
Boundary terms in the Barrett–Crane spin foam model and consistent gluing
Oriti, D. (2002) · Physics Letters B · doi:10.1016/s0370-2693(02)01559-9 · Cited by 23 · see citing works
Diffeomorphism-invariant lattice actions
Vladimirov, A. A., & Diakonov, D. (2014) · Physics of Particles and Nuclei · doi:10.1134/s1063779614040145 · Cited by 22 · see citing works
Dual variables and a connection picture for the Euclidean Barrett–Crane model
Pfeiffer, H. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/6/306 · Cited by 22 · see citing works
The Spinfoam Framework for Quantum GravityPreprint
Livine, E. R. (2010) · Cited by 22 · see citing works
Alternative symplectic structures for SO (3, 1) and SO (4) four-dimensional BF theories
Montesinos, M. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/7/004 · Cited by 19 · see citing works
Turning on gravity with the Higgs mechanism
Alexander, S., Barrow, J. D., & Magueijo, J. (2016) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/14/14lt01 · Cited by 19 · see citing works
On the Relation between Rigging Inner Product and Master Constraint Direct Integral DecompositionPreprint
Han, M., & Thiemann, T. (2010) · Cited by 19 · see citing works
Polytopes in all dimensional loop quantum gravity
Long, G., & Ma, Y. (2022) · The European Physical Journal C · doi:10.1140/epjc/s10052-022-09988-2 · Cited by 18 · see citing works
The Plebanski sectors of the EPRL vertex
Engle, J. (2011) · Classical and Quantum Gravity · doi:10.1088/0264-9381/28/22/225003 · Cited by 18 · see citing works
Note on the Plebanski action with the cosmological constant and an Immirzi parameter
Smolin, L., & Simone Speziale, D. (2010) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.81.024032 · Cited by 17 · see citing works
Spinfoam 2d quantum gravity and discrete bundles
Oriti, D., Carlo Rovelli, C., & Simone Speziale, D. (2004) · HAL · Cited by 17 · see citing works
Han, M. (2010) · Max Planck Digital Library · Cited by 16 · see citing works
1 The Plebanski sectors of the EPRL vertexPreprint
Engle, J. (2013) · Cited by 16 · see citing works
Hamiltonian analysis of pregeometric gravity
Addazi, A., Capozzıello, S., Marcianò, A., & Meluccio, G. (2025) · Physical review. D/Physical review. D. · doi:10.1103/v5wg-sy4w · Cited by 15 · see citing works
On the relation between rigging inner product and master constraint direct integral decomposition
Han, M., & Thiemann, T. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3486359 · Cited by 15 · see citing works
- Authors
- Pietri, R. D., & Freidel, L.
- Affiliations
- University of Parma (IT)
- École Normale Supérieure de Lyon (FR)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1999-01-01
- Volume
- 16
- Issue
- 7
- Pages
- 2187-2196
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2071979448
- Cited by
- 182
- References
- 20
- Citations by year
- 2026: 1 · 2025: 4 · 2024: 4 · 2023: 5 · 2022: 3 · 2021: 5 · 2020: 3 · 2019: 5 · 2018: 6 · 2016: 6 · 2015: 2 · 2014: 6 · 2013: 8 · 2012: 12
- FWCI
- 5.13
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Centre National de la Recherche Scientifique
- 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, self-dual gravity, continuum limit, quantum gravity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
