Combinatorial Space from Loop Quantum Gravity
Open accessThe 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?
Spin foam models of gravity incorporate the discreteness of the geometry of space first uncovered in loop quantized canonical theory into a spacetime sum over histories formalism naturally suited to a 4-diffeo invariant theory.
“Spin foam models of gravity incorporate the discreteness of the geometry of space first uncovered [20, 21, 22, 23, 24] in loop quantized canonical theory into a spacetime sum over histories formalism naturally suited to a 4-diffeo invariant theory.”
From Spacetime as a Feynman diagram: the connection formulation (2001) · cites this paper as [24]
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
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
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
Real Ashtekar variables for Lorentzian signature space-times
Barbero G., J. F. (1995) · Physical Review D · doi:10.1103/physrevd.51.5507 · Cited by 758 · see citing works
Black Hole Entropy from Loop Quantum Gravity
Rovelli, C. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.3288 · Cited by 660 · see citing works
Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
Ashtekar, A., Lewandowski, J., Marolf, D., Mourão, J., & Thiemann, T. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531252 · Cited by 528 · see citing works
(1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 412 · see citing works
Weaving a classical metric with quantum threads
Ashtekar, A., Rovelli, C., & Smolin, L. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.237 · Cited by 399 · see citing works
Loops, Knots, Gauge Theories and Quantum Gravity
Gambini, R., Pullin, J., & Ashtekar, A. (1996) · doi:10.1017/cbo9780511524431 · Cited by 295 · 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
Rosenfeld, L. (1972) · Nuclear Physics A · doi:10.1016/0375-9474(72)90347-8 · Cited by 275 · see citing works
Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
Thiemann, T. (1996) · Cited by 228 · 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
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
Reconstruction of gauge potentials from Wilson loops
Giles, R. (1981) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.24.2160 · Cited by 169 · see citing works
Holonomy and path structures in general relativity and Yang-Mills theory
Barrett, J. W. (1991) · International Journal of Theoretical Physics · doi:10.1007/bf00671007 · Cited by 117 · see citing works
Complex actions in two-dimensional topology change
Louko, J., & Sorkin, R. D. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1/018 · Cited by 113 · see citing works
General 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
(1992) · doi:10.1142/1555 · Cited by 62 · see citing works
The Interface of Knots and Physics
Kauffman, L. H. (1996) · Proceedings of symposia in applied mathematics · doi:10.1090/psapm/051 · Cited by 54 · see citing works
On the relation between the connection and the loop representation of quantum gravity
Pietri, R. D. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/1/009 · Cited by 50 · 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
Complex actions in two-dimensional topology change
Louko, J., & Sorkin, R. D. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 44 · see citing works
A loop representation for the quantum Maxwell field
Ashtekar, A., & Carlo Rovelli, C. (1992) · Classical and Quantum Gravity · doi:10.1088/0264-9381/9/5/002 · Cited by 40 · see citing works
A Loop Representation for the Quantum Maxwell Field
Ashtekar, A., & Carlo Rovelli, C. (1992) · CERN Document Server (European Organization for Nuclear Research) · Cited by 38 · see citing works
Moduli-space structure of knots with intersections
Grot, N., & Carlo Rovelli, C. (1996) · Journal of Mathematical Physics · doi:10.1063/1.531527 · Cited by 37 · see citing works
Outline of a generally covariant quantum field theory and a quantum theory of gravity
Rovelli, C. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531255 · Cited by 37 · 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
A combinatorial approach to diffeomorphism invariant quantum gauge theories
Zapata, J. A. (1997) · Journal of Mathematical Physics · doi:10.1063/1.532159 · Cited by 32 · see citing works
Self-citationFurther results on geometric operators in quantum gravity
Loll, R. (1997) · Classical and Quantum Gravity · doi:10.1088/0264-9381/14/7/010 · Cited by 23 · see citing works
FURTHER RESULTS ON GEOMETRIC OPERATORS IN QUANTUM GRAVITY
Loll, R. (1996) · MPG.PuRe (Max Planck Society) · Cited by 19 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
(1998) · doi:10.12942/lrr-1998-1 · Cited by 917 · see citing works
Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
Lewandowski, J., Okołów, A., Sahlmann, H., & Thiemann, T. (2006) · Communications in Mathematical Physics · doi:10.1007/s00220-006-0100-7 · Cited by 297 · 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
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
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
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
Strings, loops and others: a critical survey of the present approaches to quantum gravityPreprint
Carlo Rovelli, C. (1998) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9803024 · Cited by 68 · see citing works
Separable Hilbert space in loop quantum gravity
Fairbairn, W., & Rovelli, C. (2004) · Journal of Mathematical Physics · doi:10.1063/1.1763247 · Cited by 68 · see citing works
Separable Hilbert space in Loop Quantum GravityPreprint
Fairbairn, W. J., & Carlo Rovelli, C. (2004) · Cited by 63 · 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
Loop Quantum Gravity Phenomenology: Linking Loops to Observational Physics
Girelli, F. (2012) · Symmetry Integrability and Geometry Methods and Applications · doi:10.3842/sigma.2012.098 · Cited by 28 · see citing works
Carlo Rovelli, C. (2006) · AIP conference proceedings · doi:10.1063/1.2399564 · Cited by 29 · see citing works
Comments on the kinematical structure of loop quantum cosmology
Velhinho, J. M. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/l01 · Cited by 23 · see citing works
Dirac quantization of parametrized field theory
Varadarajan, M. (2007) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.75.044018 · Cited by 21 · see citing works
ON THE STRUCTURE OF THE SPACE OF GENERALIZED CONNECTIONS
Velhinho, J. M. (2004) · International Journal of Geometric Methods in Modern Physics · doi:10.1142/s0219887804000198 · Cited by 19 · see citing works
Shape in an atom of space: exploring quantum geometry phenomenology
Major, S. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/22/225012 · Cited by 15 · see citing works
Projective loop quantum gravity. I. State space
Lanéry, S., & Thiemann, T. (2016) · Journal of Mathematical Physics · doi:10.1063/1.4968205 · Cited by 14 · see citing works
Comments on "The kinematical structure of loop quantum cosmology"
Velhinho, J. M. (2004) · CERN Document Server (European Organization for Nuclear Research) · Cited by 14 · see citing works
String quantization: Fock vs. LQG RepresentationsPreprint
Helling, R. C., & Policastro, G. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0409182 · Cited by 14 · see citing works
Automorphisms in loop quantum gravity
Bähr, B., & Thiemann, T. (2009) · Classical and Quantum Gravity · doi:10.1088/0264-9381/26/23/235022 · Cited by 12 · see citing works
From Euclidean to Lorentzian loop quantum gravity via a positive complexifier
Varadarajan, M. (2018) · Classical and Quantum Gravity · doi:10.1088/1361-6382/aaf2cd · Cited by 10 · see citing works
Piecewise linear loop quantum gravity
Engle, J. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/3/035003 · Cited by 9 · see citing works
Canonical ``Loop'' Quantum Gravity and Spin Foam ModelsPreprint
Pietri, R. D. (1999) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9903076 · Cited by 9 · see citing works
Projective limits of state spaces IV. Fractal label sets
Lanéry, S., & Thiemann, T. (2017) · Journal of Geometry and Physics · doi:10.1016/j.geomphys.2017.08.008 · Cited by 6 · see citing works
FUNCTORIAL ASPECTS OF THE SPACE OF GENERALIZED CONNECTIONS
Velhinho, J. M. (2005) · Modern Physics Letters A · doi:10.1142/s0217732305017767 · Cited by 5 · see citing works
Canonical “Loop” Quantum Gravity and Spin Foam Models
Pietri, R. D. (2000) · Springer eBooks · doi:10.1007/978-88-470-2113-6_6 · Cited by 5 · see citing works
Effective loop quantized theories
Zapata, J. A. (2005) · Journal of Physics Conference Series · doi:10.1088/1742-6596/24/1/003 · Cited by 1 · see citing works
Self-citationA proposal for renormalization without a background metric
Manrique, E. (2005) · Journal of Physics Conference Series · doi:10.1088/1742-6596/24/1/004 · Cited by 1 · see citing works
Automorphismsin Loop Quantum Gravity
PIfavitationsphysik, M. (2013)
Matter Spin Networks and Gauge Invariance at Planck Scales
Altaĭsky, M. V. (2026) · International Journal of Theoretical Physics · doi:10.1007/s10773-026-06304-6
- Authors
- Zapata, J. A.
- Venue
- General Relativity and Gravitation
- Published
- 1998-08
- Volume
- 30
- Issue
- 8
- Pages
- 1229-1245
- ISSN
- 0001-7701 (ISSN-L)
- 1572-9532
- OpenAlex
- W1640215051
- Cited by
- 31
- References
- 31
- Citations by year
- 2026: 1 · 2018: 1 · 2017: 1 · 2016: 1 · 2015: 1 · 2013: 1 · 2012: 1
- FWCI
- 1.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- General Relativity and Gravitation (publishedVersion)
- arXiv (Cornell University) (publishedVersion)
- 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 › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Keywords
- loop quantum gravity, canonical quantization, diffeomorphism invariance, Yang-Mills fields, algebra of observables, quantum gravity, gauge theory
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