Non-perturbative solutions for lattice 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?
The existence of this quantization ambiguity is due to the peculiar kind of representation on which nonperturbative quantum gravity is based.
“The existence of this quantization ambiguity is due to the peculiar kind of representation on which nonperturbative quantum gravity is based [5,6].”
From Immirzi parameter in quantum general relativity (1998) · cites this paper as [5]
This representation is characterized by the fact that the holonomy is a well-defined operator in the quantum theory.
“This representation is characterized by the fact that the holonomy is a well-defined operator in the quantum theory.”
From Immirzi parameter in quantum general relativity (1998) · cites this paper as [5]
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
Hamiltonian formulation of Wilson's lattice gauge theories
Kogut, J., & Susskind, L. (1975) · Physical Review D · doi:10.1103/physrevd.11.395 · Cited by 2,021 · see citing works
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
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
Creutz, M. J. (2022) · Cambridge University Press eBooks · doi:10.1017/9781009290395 · Cited by 1,007 · see citing works
Lectures on Non-Perturbative Canonical Gravity
Ashtekar, A. (1991) · Advanced Series in Astrophysics and Cosmology · doi:10.1142/1321 · Cited by 872 · 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
The lattice gauge theory approach to quantum chromodynamics
Kogut, J. B. (1983) · Reviews of Modern Physics · doi:10.1103/revmodphys.55.775 · Cited by 546 · see citing works
A Monte Carlo study of SU(2) Yang-Mills theory at finite temperature
McLerran, L., & Svetitsky, B. (1981) · Physics Letters B · doi:10.1016/0370-2693(81)90986-2 · Cited by 488 · see citing works
Monte Carlo study of SU(2) gauge theory at finite temperature
Kuti, J., Polonyi, J., & Szlachányi, K. (1981) · Physics Letters B · doi:10.1016/0370-2693(81)90987-4 · Cited by 442 · see citing works
Projective techniques and functional integration for gauge theories
Ashtekar, A., & Lewandowski, J. (1995) · Journal of Mathematical Physics · doi:10.1063/1.531037 · Cited by 388 · see citing works
The Segal-Bargmann "Coherent State" Transform for Compact Lie Groups
Hall, B. C. (1994) · Journal of Functional Analysis · doi:10.1006/jfan.1994.1064 · Cited by 330 · 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
Jones polynomials for intersecting knots as physical states of quantum gravity
Brügmann, B., Gambini, R., & Pullin, J. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90060-o · Cited by 98 · see citing works
Three-plus-one formulation of Regge calculus
Piran, T., & Williams, R. M. (1986) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.33.1622 · Cited by 63 · see citing works
Covariant factor ordering of gauge systems
Kucha, K. V. (1986) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.34.3044 · Cited by 55 · see citing works
A lattice approach to spinorial quantum gravity
Renteln, P., & Smolin, L. (1989) · Classical and Quantum Gravity · doi:10.1088/0264-9381/6/3/009 · Cited by 53 · see citing works
Intersecting 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 52 · see citing works
3+1 Regge calculus with conserved momentum and Hamiltonian constraints
Friedman, J. L., & Jack, I. (1986) · Journal of Mathematical Physics · doi:10.1063/1.527224 · Cited by 51 · see citing works
Intersecting-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
Independent SU(2)-loop variables and the reduced configuration space of SU(2)-lattice gauge theory
Loll, R. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90200-u · Cited by 30 · see citing works
Self-citationYang-Mills theory without Mandelstam constraints
Loll, R. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90400-j · Cited by 30 · see citing works
Self-citationSome results of SU(2) spinorial lattice gravity
Renteln, P. (1990) · Classical and Quantum Gravity · doi:10.1088/0264-9381/7/3/023 · Cited by 23 · see citing works
Recent Mathematical Developments in Quantum General RelativityPreprint
Ashtekar, A. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9411055 · Cited by 13 · see citing works
A New Discretization of Classical and Quantum General RelativityPreprint
Boström, O., Miller, M., & Smolin, L. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9304005 · Cited by 10 · see citing works
Simplical gravity and random surfaces
Jurkiewicz, J. (1993) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(93)90181-5 · Cited by 5 · see citing works
Gauge-invariant variables and mandelstam constraints in SU(2) gauge theory
Watson, N. J. (1995) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/0920-5632(95)00073-i · Cited by 4 · see citing works
Flagged first, then by citations
1 of the 28 references couldn’t be matched to a known paper.
Research works printed but not linked: 2
- [7][7] Br¨ ugmann, B.: Loop representations, in Canonical gravity: from classical to quantum , ed. J. Ehlers and H. Friedrich, Lecture Notes in Physics 434, Springer, Berlin, 1994 -
- [13][13] Ashtekar, A., Lewandowski, L., Marolf, D., Mour˜ ao, J. and Thiemann, T.: Coherent state transform for spaces of connections, preprint Penn State U., Dec 1994, e-Print Archive: gr-qc 9412014 -
Cited by
Sorted by citations
(1998) · doi:10.12942/lrr-1998-1 · Cited by 917 · see citing works
Quantum gravity and Regge calculus
Immirzi, G. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00354-x · Cited by 287 · see citing works
1 Quantum Gravity and Regge CalculusPreprint
Immirzi, G. (1997) · Cited by 268 · see citing works
Discrete Approaches to Quantum Gravity in Four Dimensions
Loll, R. (1998) · Living Reviews in Relativity · doi:10.12942/lrr-1998-13 · Cited by 232 · see citing works
Self-citationImmirzi parameter in quantum general relativity
Rovelli, C., & Thiemann, T. (1998) · Physical Review D · doi:10.1103/physrevd.57.1009 · Cited by 171 · see citing works
Volume Operator in Discretized Quantum Gravity
Loll, R. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.3048 · Cited by 124 · see citing works
Self-citation<i>SO</i> (4, <i>C</i> )-covariant Ashtekar-Barbero gravity and the Immirzi parameter
Alexandrov, S. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/20/307 · Cited by 112 · see citing works
Geometric Quantization¶and the Generalized Segal--Bargmann Transform¶for Lie Groups of Compact Type
Hall, B. C. (2002) · Communications in Mathematical Physics · doi:10.1007/s002200200607 · Cited by 93 · see citing works
Quantum geometry with intrinsic local causality
Markopoulou, F., & Smolin, L. (1998) · Physical Review D · doi:10.1103/physrevd.58.084032 · Cited by 95 · 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
Self-citationA 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
Area spectrum in Lorentz covariant loop gravity
Alexandrov, S., & Vassilevich, D. (2001) · Physical Review D · doi:10.1103/physrevd.64.044023 · Cited by 68 · see citing works
Harmonic analysis with respect to heat kernel measure
Hall, B. C. (2000) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-00-00886-7 · Cited by 64 · see citing works
Hall, B. C., Mitchell, J. J., Jeffrey, & Mitchell, J. (2001) · Cited by 63 · see citing works
Hall, B. C., & Mitchell, J. J. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1446664 · Cited by 63 · 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
Self-citationMatrix 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
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
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
The Small Scale Structure of Space-Time: A Bibliographical ReviewPreprint
Gibbs, P. E. (1995) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/9506171 · Cited by 51 · see citing works
The Segal–Bargmann Transform for Path-Groups
Hall, B. C., & Sengupta, A. N. (1998) · Journal of Functional Analysis · doi:10.1006/jfan.1997.3159 · Cited by 36 · see citing works
Combinatorial Space from Loop Quantum Gravity
Zapata, J. A. (1998) · General Relativity and Gravitation · doi:10.1023/a:1026699012787 · Cited by 31 · see citing works
Simplifying the spectral analysis of the volume operator
Loll, R. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00334-9 · Cited by 27 · 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
Topological lattice gravity using self-dual variables
Zapata, J. A. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/10/003 · Cited by 26 · see citing works
On The Diffeomorphism-Commutators Of Lattice Quantum GravityPreprint
Loll, R. (1997) · Cited by 26 · see citing works
Self-citationOn the diffeomorphism commutators of lattice quantum gravity
Loll, R. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/008 · Cited by 25 · see citing works
Self-citationLattice 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
Strings as perturbations of evolving spin-networksPreprint
Smolin, L. (2000) · Cited by 23 · see citing works
Real 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
Self-citationFURTHER RESULTS ON GEOMETRIC OPERATORS IN QUANTUM GRAVITY
Loll, R. (1996) · MPG.PuRe (Max Planck Society) · Cited by 19 · see citing works
Self-citationImmirzi, G. (1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 19 · see citing works
Quantum gravity as a “sum over surfaces”
Rovelli, C. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00351-4 · Cited by 18 · see citing works
Further 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
Self-citationImmirzi, G. (1996) · Classical and Quantum Gravity · doi:10.1088/0264-9381/13/9/006 · 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
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
Towards a background independent approach to M theoryPreprint
Smolin, L. (1998) · 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
On diffeomorphism invariance for lattice theories
Corichi, A., & Zapata, R. J. A. (1996) · CERN Document Server (European Organization for Nuclear Research) · Cited by 10 · see citing works
On diffeomorphism invariance for lattice theories
Corichi, A., & Zapata, J. (1997) · Nuclear Physics B · doi:10.1016/s0550-3213(97)00141-7 · Cited by 9 · see citing works
Strings as perturbations of evolving spin networks
Smolin, L. (2000) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(00)00758-1 · Cited by 10 · see citing works
Loll, R. (1997) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(97)00398-8 · Cited by 6 · see citing works
Self-citationTowards a background independent approach to M theory
Smolin, L. (1999) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(98)00206-9 · Cited by 10 · see citing works
Modelling gravity on a hyper-cubic lattice
Tate, K., & Visser, M. (2012) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.86.124003 · Cited by 3 · see citing works
Making quantum gravity calculablePreprint
Loll, R. (1995) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9511080 · Cited by 1 · see citing works
Self-citation
- Authors
- Loll, R.
- Affiliations
- Istituto Nazionale di Fisica Nucleare, Sezione di Firenze (IT)
- Corresponding author
- Loll, R.
- ORCID
- Loll, R.
- Venue
- Nuclear Physics B
- Publisher
- Elsevier BV
- Published
- 1995-06
- Volume
- 444
- Issue
- 3
- Pages
- 619-639
- ISSN
- 0550-3213 (ISSN-L)
- OpenAlex
- W2091923127
- Cited by
- 47
- References
- 28
- Citations by year
- 2012: 1
- FWCI
- 9.35
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Nuclear Physics B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- 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
- lattice gravity, canonical quantum gravity, Wilson loops, Polyakov loop, Wheeler-DeWitt equation, non-perturbative solutions, gauge invariance, diffeomorphism invariance, kinematical Hilbert space, four-dimensional spacetime
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