Quantum geometry with intrinsic local causality
Open accessAbstract
The space of states and operators for a large class of background independent theories of quantum spacetime dynamics is defined. The SU(2) spin networks of quantum general relativity are replaced by labelled compact two-dimensional surfaces. The space of states of the theory is the direct sum of the spaces of invariant tensors of a quantum group ${G}_{q}$ over all compact (finite genus) oriented 2-surfaces. The dynamics is background independent and locally causal. The dynamics constructs histories with discrete features of spacetime geometry such as causal structure and multifingered time. For SU(2) the theory satisfies the Bekenstein bound and the holographic hypothesis is recast in this formalism.
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?
Markopoulou and Smolin define a general class of causal spin-foam models for gravity using the kinematical setting of LQG and assuming a micro-local causal structure at the Planck scale.
“Using the kinematical setting of LQG with the assumption of the existence of a micro-local (in the sense of Planck scale) causal structure, Markopoulou and Smolin define a general class of (causal) spin-foam models for gravity [267, 264] (see also [268]).”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [268]
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
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
Susskind, L. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531249 · Cited by 4,085 · see citing works
Thermodynamics of Spacetime: The Einstein Equation of State
Jacobson, T. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.1260 · Cited by 2,603 · see citing works
String theory dynamics in various dimensions
Witten, E. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00158-o · Cited by 2,112 · see citing works
String theory dynamics in various dimensionsPreprint
Witten, E. (1995) · Cited by 1,754 · see citing works
Fusion rules and modular transformations in 2D conformal field theory
Verlinde, E. (1988) · Nuclear Physics B · doi:10.1016/0550-3213(88)90603-7 · Cited by 1,537 · see citing works
Invariants of 3-manifolds via link polynomials and quantum groups
Reshetikhin, N., & Turaev, V. G. (1991) · Inventiones Mathematicae · doi:10.1007/bf01239527 · Cited by 1,492 · see citing works
Unity of superstring dualities
HULL, C. M., & Townsend, P. K. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(94)00559-w · Cited by 1,449 · see citing works
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 · cited 8× · see citing works
“This interpretation will be developed in the next section, where we will see that an example in the case of SU(2) is given by the area operator obtained in quantum general relativity [11, 2].”
BackgroundMethodInfluentialSelf-citationClassical and quantum conformal field theory
Moore, G., & Seiberg, N. (1989) · Communications in Mathematical Physics · doi:10.1007/bf01238857 · Cited by 1,327 · see citing works
Unity of superstring dualities
Hull, C. M., & Townsend, P. K. (1994) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,202 · see citing works
State sum invariants of 3-manifolds and quantum 6j-symbols
Turaev, V. G., & Viro, O. Y. (1992) · Topology · doi:10.1016/0040-9383(92)90015-a · Cited by 1,145 · see citing works
Ribbon graphs and their invaraints derived from quantum groups
Reshetikhin, N., & Turaev, V. G. (1990) · Communications in Mathematical Physics · doi:10.1007/bf02096491 · Cited by 1,066 · see citing works
Bombelli, L., Lee, J., Meyer, D., & Sorkin, R. D. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.521 · Cited by 1,012 · see citing works
(1998) · doi:10.12942/lrr-1998-1 · Cited by 917 · 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
Self-citationBlack hole entropy in canonical quantum gravity and superstring theory
Susskind, L., & Uglum, J. (1994) · Physical Review D · doi:10.1103/physrevd.50.2700 · Cited by 754 · 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
Self-citationThe quantum mass spectrum of the Kerr black hole
Bekenstein, J. D. (1974) · Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento · doi:10.1007/bf02762768 · Cited by 584 · 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
Self-citationRelativistic Spin Networks and Quantum GravityPreprint
Barrett, J. W., Crane, L., & Crane, J. W. B. L. (1998) · Cited by 423 · see citing works
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/5/012 · Cited by 416 · 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
“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
P.L. Homeomorphic Manifolds are Equivalent by Elementary 5hellingst
Pachner, U. (1991) · European Journal of Combinatorics · doi:10.1016/s0195-6698(13)80080-7 · Cited by 351 · see citing works
Black hole condensation and the unification of string vacua
Greene, B. R., Morrison, D. R., & Strominger, A. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00371-x · Cited by 279 · see citing works
Rosenfeld, L. (1972) · Nuclear Physics A · doi:10.1016/0375-9474(72)90347-8 · Cited by 275 · see citing works
Black Hole Condensation And The Unification Of String Vacua
GREENE, B. R., Morrison, D. R., & Strominger, A. (1995) · Cited by 268 · see citing works
Calabi-Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String TheoryPreprint
Aspinwall, P. S., GREENE, B. R., & Morrison, D. R. (1993) · Cited by 256 · see citing works
Calabi-Yau moduli space, mirror manifolds and spacetime topology change in string theory
Aspinwall, P. S., Greene, B. R., & Morrison, D. R. (1994) · Nuclear Physics B · doi:10.1016/0550-3213(94)90321-2 · Cited by 249 · 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
Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
Kauffman, L. H., & Lins, S. (1994) · doi:10.1515/9781400882533 · Cited by 245 · 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
Self-citationString theory and the principle of black hole complementarity
Susskind, L. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.2367 · Cited by 232 · see citing works
The physical Hamiltonian in nonperturbative quantum gravity
Rovelli, C., & Smolin, L. (1994) · Physical Review Letters · doi:10.1103/physrevlett.72.446 · Cited by 215 · see citing works
Self-citationGeometry 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
Strings, black holes, and Lorentz contraction
Susskind, L. (1994) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.49.6606 · Cited by 191 · see citing works
Kinematical Hilbert spaces for fermionic and Higgs quantum field theories
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/6/006 · Cited by 184 · see citing works
Sen, A. (1998) · Journal of High Energy Physics · doi:10.1088/1126-6708/1998/03/005 · Cited by 167 · see citing works
A length operator for canonical quantum gravity
Thiemann, T. (1998) · Journal of Mathematical Physics · doi:10.1063/1.532445 · Cited by 156 · see citing works
A comment on quantum group symmetry in conformal field theory
Moore, G. W., & Reshetikhin, N. (1989) · Nuclear Physics B · doi:10.1016/0550-3213(89)90219-8 · Cited by 151 · see citing works
A Length Operator for Canonical Quantum Gravity
Thiemann, T. (1996) · Cited by 151 · see citing works
Causal evolution of spin networks
Markopoulou, F., & Smolin, L. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)80019-3 · Cited by 134 · see citing works
Self-citationMultiple mirror manifolds and topology change in string theory
Aspinwall, P. S., Greene, B. R., & Morrison, D. R. (1993) · Physics Letters B · doi:10.1016/0370-2693(93)91428-p · Cited by 107 · see citing works
Quantum deformation of quantum gravity
Major, S., & Smolin, L. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(96)00259-3 · Cited by 103 · see citing works
Self-citationNew variables for canonical supergravity
Ted Jacobson, A. (1988) · Classical and Quantum Gravity · doi:10.1088/0264-9381/5/6/012 · Cited by 101 · see citing works
Crane, L. (1991) · Communications in Mathematical Physics · doi:10.1007/bf02104124 · Cited by 98 · see citing works
Multiple mirror manifolds and topology change in string theory
Aspinwall, P. S., GREENE, B. R., & Morrison, D. R. O. (1993) · CERN Document Server (European Organization for Nuclear Research) · Cited by 91 · see citing works
Spectrum of the volume operator in quantum gravity
Loll, R. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(95)00627-3 · Cited by 90 · see citing works
Quantum Gravity: A Fundamental Problem and Some Radical Ideas
Hooft, G. ’. (1979) · Springer eBooks · doi:10.1007/978-1-4613-2955-8_8 · Cited by 87 · see citing works
Quantum Deformation of Quantum Gravity
Major, S., & Smolin, L. (1995) · Cited by 79 · 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
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
The geometry of quantum spin networks
Borissov, R., Major, S., & Smolin, L. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/12/009 · Cited by 68 · see citing works
Self-citationOn the consistency of the constraint algebra in spin network quantum gravity
Gambini, R., Lewandowski, J., Marolf, D. M., & Pullin, J. A. (1997) · Civil War Book Review · Cited by 65 · see citing works
ON ALGEBRAIC STRUCTURES IMPLICIT IN TOPOLOGICAL QUANTUM FIELD THEORIES
Crane, L., & Yetter, D. N. (1999) · Journal of Knot Theory and Its Ramifications · doi:10.1142/s0218216599000109 · Cited by 64 · see citing works
Spectrum of the volume operator in quantum gravity
Loll, R. (1996) · Utrecht University Repository (Utrecht University) · Cited by 59 · see citing works
Non-perturbative solutions for lattice quantum gravity
Loll, R. (1995) · Nuclear Physics B · doi:10.1016/0550-3213(95)00184-t · Cited by 47 · see citing works
Towards a loop representation for quantum canonical supergravity
Armand-Ugon, D., Gambini, R., Obregón, O., & Pullin, J. A. (1996) · Nuclear Physics B · doi:10.1016/0550-3213(95)00582-x · Cited by 47 · see citing works
Ashtekar's Formulation for N = 1, 2 Supergravities as "Constrained" BF Theories
Ezawa, K. (1996) · Progress of Theoretical Physics · doi:10.1143/ptp.95.863 · Cited by 41 · see citing works
The non-perturbative canonical quantization of the N = 1 supergravity
Sano, T., & Shiraishi, J. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90442-r · Cited by 40 · see citing works
The future of spin networksPreprint
Smolin, L. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9702030 · Cited by 33 · see citing works
Self-citationThe classical limit and the form of the hamiltonian constraint in nonperturbative quantum gravity
Smolin, L. (1996) · arXiv · doi:10.48550/arxiv.gr-qc/9609034 · Cited by 33 · see citing works
Self-citationGraphical evolution of spin network states
Borissov, R. (1997) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.55.6099 · Cited by 27 · see citing works
Strings as perturbations of evolving spin-networksPreprint
Smolin, L. (2000) · Cited by 23 · see citing works
Self-citationThe Ashtekar Formulation for CanonicalN= 2 Supergravity
Kunitomo, H., & Sano, T. (1993) · Progress of Theoretical Physics Supplement · doi:10.1143/ptps.114.31 · Cited by 22 · see citing works
Conformal field theory, spin geometry, and quantum gravity
Crane, L. (1991) · Physics Letters B · doi:10.1016/0370-2693(91)90823-9 · Cited by 21 · see citing works
The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Field TheoryPreprint
Smolin, L. (1995) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9508064 · Cited by 17 · see citing works
Self-citationN=3 and N=4 Two-Form Supergravities
Kadoyoshi, T., & Nojiri, S. (1997) · Modern Physics Letters A · doi:10.1142/s0217732397001199 · Cited by 15 · see citing works
The Bekenstein bound, topological quantum field theory and pluralistic quantum cosmologyPreprint
Smolin, L. (1995) · Cited by 15 · see citing works
Self-citationWHEATER, J. F. (1989) · Physics Letters B · doi:10.1016/0370-2693(89)91631-6 · Cited by 14 · see citing works
Flagged first, then by citations
Research works printed but not linked: 10
- [11][11] L Smolin: in Quantum Gravity and Cosmology , eds J P´ erez-Mercader et al , World Scientific, Singapore 1992. -
- [16][16] T. Thiemann, Quantum spin dynamics I, Harvard preprint (1996), grqc/9606089; Quantum spin dynamics II, Harvard preprint (1996), grqc/9606090. -
- [23][23] F. Markopoulou, Dual formulation of spin network evolution grqc/9704013, CGPG preprint (1997). -
- [30][30] L. Kauffman and S. Lins Tempereley-Lieb Recoupling Theory and Invariants of 3-Manifolds Princeton University Press, 1994, and references therein. -
- [35][35] G. 'tHooft, Dimensional reduction in quantum gravity gr-qc/9310006. - · arXiv
- [47][47] S. Gupta, preprint in preparation. -
- [49][49] A. Sen String networks , hep-th/9711130. - · arXiv
- [50][50] F. Markopoulou and L. Smolin, Models of evolving spin networks preprint in preparation. -
- [51][51] S. Kauffman and L. Smolin, Evolving spin networks as discrete dynamical systems , preprint in preparation. -
- [52][52] See, for example, J. Hartle, Spacetime Quantum Mechanics and the Quantum Mechanics of Spacetime , gr-qc/9304006; M. Gell-Mann and J. Hartle, Strong Decoherence , gr-qc/9509054; C. J. Isham, Topos Theory and Consistent Histories: The Internal Logic of the Set of all Consistent Sets , gr-qc/9607069, Int.J.Theor.Phys. 36 (1997) 785-814; Quantum logic and decohering histories , quant-ph/9506028. <!-- image --> <!-- image --> <!-- image --> · arXiv
Cited by
Sorted by citations
Bousso, R. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.825 · Cited by 1,741 · 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
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
Holography in general space-times
Raphael Bousso, A. (1999) · Journal of High Energy Physics · doi:10.1088/1126-6708/1999/06/028 · Cited by 409 · 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
Carlo Rovelli, C. (2006) · The frontiers collection · doi:10.1007/978-3-319-55420-4_10 · Cited by 347 · see citing works
Lectures on Loop Quantum GravityPreprint
Thiemann, T. (2003) · Cited by 286 · see citing works
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
Loop quantum gravity: An outside viewPreprint
Nicolai, H., Peeters, K., & Zamaklar, M. (2005) · Cited by 230 · see citing works
Gauge field theory coherent states (GCS): II. Peakedness properties
Thiemann, T., & Winkler, O. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/14/301 · Cited by 192 · see citing works
Gauge field theory coherent states (GCS): I. General properties
Thiemann, T. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/11/304 · Cited by 233 · see citing works
Spacetime as a Feynman diagram: the connection formulation
Reisenberger, M. P., & Rovelli, C. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/1/308 · Cited by 202 · 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
Loop quantum gravity: an outside view
Nicolai, H., Peeters, K., & Zamaklar, M. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/19/r01 · Cited by 176 · 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
Gauge Field Theory Coherent States (GCS): I. General Properties
Thiemann, T. (2000) · Cited by 147 · see citing works
AN INVITATION TO LOOP QUANTUM GRAVITY
Smolin, L. (2004) · International Symposium on Quantum Theory and Symmetries (QTS) · doi:10.1142/9789812702340_0078 · Cited by 155 · see citing works
Self-citationGauge field theory coherent states (GCS): III. Ehrenfest theorems
Thiemann, T., & Winkler, O. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/21/315 · Cited by 126 · see citing works
Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit
Thiemann, T., & Winkler, O. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/23/302 · Cited by 126 · see citing works
Quantum gravity with a positive cosmological constantPreprint
Smolin, L. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0209079 · Cited by 152 · see citing works
Self-citationThiemann, T. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/17/301 · Cited by 102 · see citing works
Quantum gravity and the standard model
Bilson-Thompson, S. O., Markopoulou, F., & Smolin, L. (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 104 · see citing works
Self-citationGauge field theory coherent states (GCS) III: Ehrenfest theoremsPreprint
Thiemann, T., & Winkler, O. (2001) · Cited by 112 · see citing works
Raphael Bousso, A. (2003) · Springer eBooks · doi:10.1007/978-94-010-0211-0_3 · Cited by 131 · see citing works
Higher-dimensional algebra and Planck scale physics
Baez, J. C. (2001) · Cambridge University Press eBooks · doi:10.1017/cbo9780511612909.009 · Cited by 100 · see citing works
How far are we from the quantum theory of gravity?Preprint
Smolin, L. (2003) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0303185 · Cited by 121 · see citing works
Self-citationCoarse graining in spin foam models
Markopoulou, F. (2003) · Classical and Quantum Gravity · doi:10.1088/0264-9381/20/5/301 · Cited by 92 · see citing works
Self-citationHaggard, H. M., Han, M., Kamiński, W., & Riello, A. (2015) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2015.08.023 · Cited by 80 · see citing works
Markopoulou, F. (2000) · CERN Document Server (European Organization for Nuclear Research) · Cited by 74 · see citing works
Self-citationQuantum gravity and the standard model
Bilson-Thompson, S. O., Markopoulou, F., & Smolin, L. (2007) · Classical and Quantum Gravity · doi:10.1088/0264-9381/24/16/002 · Cited by 69 · see citing works
Self-citationCausal structures and causal boundaries
García-Parrado, A., & Senovilla, J. M. M. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/9/r01 · Cited by 62 · see citing works
Causal structures and causal boundariesPreprint
García-parrado, A., & Senovilla, J. M. M. (2005) · Cited by 59 · see citing works
Gravitational edge modes: from Kac–Moody charges to Poincaré networks
Freidel, L., Livine, E. R., & Pranzetti, D. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab40fe · Cited by 58 · see citing works
Haggard, H. M., Han, M., Kamiński, W., & Riello, A. (2015) · Physics Letters B · doi:10.1016/j.physletb.2015.11.058 · Cited by 56 · see citing works
Wüthrich, C. (2006) · D-Scholarship@Pitt (University of Pittsburgh) · 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
Quantum-coherent mixtures of causal relations
MacLean, J.-P. W., Ried, K., Spekkens, R. W., & Resch, K. J. (2017) · Nature Communications · doi:10.1038/ncomms15149 · Cited by 52 · 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
Supersymmetric spin networks and quantum supergravity
Ling, Y., & Smolin, L. (2000) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.61.044008 · Cited by 53 · see citing works
Self-citationLoop quantum gravity and quanta of space: a primerPreprint
Carlo Rovelli, C., & Upadhya, P. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9806079 · Cited by 54 · see citing works
The strong and weak holographic principlesPreprint
Smolin, L., & Bounds, I. E. (2001) · Cited by 44 · see citing works
Self-citationStatistical Lorentzian geometry and the closeness of Lorentzian manifolds
Bombelli, L. (2000) · Journal of Mathematical Physics · doi:10.1063/1.1288494 · Cited by 41 · see citing works
The strong and weak holographic principles
Smolin, L. (2001) · Nuclear Physics B · doi:10.1016/s0550-3213(01)00049-9 · Cited by 40 · see citing works
Self-citationNull Cones and Einstein's Equations in Minkowski Spacetime
Pitts, J. B., & Schieve, W. C. (2004) · Foundations of Physics · doi:10.1023/b:foop.0000019582.44548.6a · Cited by 31 · see citing works
Propagation and interaction of chiral states in quantum gravity
Smolin, L., & Wan, Y. (2008) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2007.12.018 · 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
Holography in a quantum spacetimePreprint
Markopoulou, F., & Smolin, L. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9910146 · Cited by 29 · see citing works
Self-citationEleven-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
Self-citation(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces
Dittrich, B. (2017) · Journal of High Energy Physics · doi:10.1007/jhep05(2017)123 · Cited by 28 · see citing works
Planck-scale models of the universe
Markopoulou, F. (2004) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814990.027 · Cited by 26 · see citing works
Self-citationNull Cones and Einstein's Equations in Minkowski SpacetimePreprint
Pitts, J. B., & Schieve, W. C. (2004) · Cited by 26 · see citing works
An algebraic approach to coarse grainingPreprint
Markopoulou, F. (2000) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0006199 · Cited by 25 · see citing works
Self-citationQuantum gravity as a Fermi liquidPreprint
Alexander, S., & Calcagni, G. (2016) · Cited by 25 · see citing works
Nonperturbative dynamics for abstract (p,q) string networks
Markopoulou, F., & Smolin, L. (1998) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.58.084033 · Cited by 22 · see citing works
Self-citationKirilyuk, A. P. (2002) · arXiv (Cornell University) · Cited by 18 · see citing works
Four Principles for Quantum Gravity
Smolin, L. (2017) · Fundamental theories of physics · doi:10.1007/978-3-319-51700-1_26 · Cited by 16 · see citing works
Self-citationCandidate 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
Self-citationCombinatorial dynamics in quantum gravityPreprint
Kauffman, S. A., & Smolin, L. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9809161 · Cited by 16 · see citing works
Self-citationFrom coarse-graining to holography in loop quantum gravity
Livine, E. R. (2018) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/123/10001 · Cited by 15 · see citing works
Combinatorial Dynamics and Time in Quantum Gravity
Kauffman, S. A., & Smolin, L. (2007) · Springer eBooks · doi:10.1007/3-540-46634-7_5 · Cited by 14 · see citing works
Self-citationFree vacuum for loop quantum gravity
Conrady, F. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/16/010 · Cited by 13 · see citing works
Loop Quantum Gravity and planck Scale Phenomenology
Smolin, L. (2005) · Springer eBooks · doi:10.1007/11377306_11 · Cited by 11 · see citing works
Self-citationGauge fixing in causal dynamical triangulations
Markopoulou, F., & Smolin, L. (2006) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2006.01.009 · Cited by 12 · see citing works
Self-citationMalyshev, V. A. (2000) · Journal of Mathematical Physics · doi:10.1063/1.533357 · Cited by 10 · see citing works
Conserved quantities in background independent theories
Markopoulou, F. (2007) · Journal of Physics Conference Series · doi:10.1088/1742-6596/67/1/012019 · Cited by 9 · see citing works
Self-citationArea propagator and boosted spin networks in loop quantum gravity
Livine, E. R. (2019) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ab32d4 · Cited by 9 · see citing works
Holographic entanglement in spin network states: A focused review
Colafranceschi, E., & Adesso, G. (2022) · AVS Quantum Science · doi:10.1116/5.0087122 · Cited by 9 · see citing works
Knot theory and a physical state of quantum gravity
Liko, T., & Kauffman, L. H. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/4/r01 · Cited by 9 · see citing works
Conserved topological defects in non-embedded graphs in quantum gravity
Markopoulou, F., & Prémont-Schwarz, I. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/20/205015 · Cited by 9 · see citing works
Self-citationBibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
Corichi, A., & Hauser, A. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0509039 · Cited by 9 · see citing works
Ling, Y. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1421423 · Cited by 8 · see citing works
Causal Structure in Spin Foams
Eugenio Bianchi, A., & Martin-Dussaud, P. (2024) · Universe · doi:10.3390/universe10040181 · Cited by 7 · see citing works
Cones and causal structures on topological and differentiable manifolds
Rainer, M. (1999) · Journal of Mathematical Physics · doi:10.1063/1.533108 · Cited by 6 · see citing works
The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity
Montesinos, M., & Carlo Rovelli, C. (1998) · CERN Document Server (European Organization for Nuclear Research) · Cited by 5 · see citing works
Baez, J. C. (2003) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/318/05541 · Cited by 5 · see citing works
Invariants of Braided Ribbon NetworksPreprint
Hackett, J. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1106.5096 · Cited by 5 · see citing works
Symmetric vertex models on planar random graphs
Johnston, D. A. (1999) · Physics Letters B · doi:10.1016/s0370-2693(99)00948-x · Cited by 4 · see citing works
A unified framework for graph algebras and quantum causal historiesPreprint
Kribs, D. W. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0501087 · Cited by 4 · see citing works
Spin foam models: the dynamics of quantum geometry
Freidel, L., & Ryan, J. P. (2008) · Classical and Quantum Gravity · doi:10.1088/0264-9381/25/11/114004 · Cited by 3 · see citing works
Symmetric Vertex Models on Planar Random GraphsPreprint
Johnston, D. A. (2013) · Cited by 3 · see citing works
Causal spinfoam vertex for 4D Lorentzian quantum gravity
Eugenio Bianchi, A., Chen, C., & Gamonal, M. (2026) · Physical review. D/Physical review. D. · doi:10.1103/fwql-t4yr · Cited by 1 · see citing works
Teorías relacionales sobre la estructura del espacio-tiempo: física, filosofía, teología
Lorente, M. (2015) · DOAJ (DOAJ: Directory of Open Access Journals) · Cited by 1 · see citing works
Nonultralocality and causality in the relational framework of canonical quantum gravity
de Vegvar, P. G. N. (2016) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.93.104038 · Cited by 1 · see citing works
Causal spin foams and the ontology of spacetimePreprint
Lorente, M. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0712.1600 · Cited by 1 · see citing works
Semiclassical analysis of loop quantum gravity
Conrady, F. (2006) · edoc Publication server (Humboldt University of Berlin) · doi:10.18452/15549
Topology in Fundamental Physics
Hackett, J. (2011) · UWSpace (University of Waterloo)
Bounds on quantum cellular automaton lattice spacing from data on Lorentz violation
Mlodinow, L. D., & Brun, T. A. (2025) · Physical review. D/Physical review. D. · doi:10.1103/5w6s-jr1d
Entropy Bounds and Capacity-Limited Information Flow in Black-Hole Evaporation
Bolotin, A. (2026) · Entropy · doi:10.3390/e28060671
Toller matrices and the Feynman i ϵ in spinfoams
Eugenio Bianchi, A., Chen, C., & Gamonal, M. (2026) · Physical review. D/Physical review. D. · doi:10.1103/v3kc-4n3n
- Authors
- Markopoulou, F., & Smolin, L.
- Affiliations
- Pennsylvania State University (US)
- ORCID
- Smolin, Lee
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1998-09-28
- Volume
- 58
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2109518449
- Cited by
- 95
- References
- 73
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 1 · 2022: 1 · 2019: 2 · 2018: 1 · 2017: 3 · 2016: 2 · 2015: 3 · 2013: 2
- FWCI
- 9.90
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (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
- quantum spacetime, background independence, local causality, spin networks, quantum groups, invariant tensors, quantum general relativity, Bekenstein bound, causal structure
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
