Finite spin-foam-based theory of three- and four-dimensional quantum gravity
Open accessAbstract
Starting from Ooguri's construction for $\mathrm{BF}$ theory in three (and four) dimensions, we show how to construct a well defined theory with an infinite number of degrees of freedom. The spin network states that are kept invariant by the evolution operators of the theory are exact solutions of the Hamiltonian constraint of quantum gravity proposed by Thiemann. The resulting theory is the first example of a well defined, finite, consistent, spin-foam-based theory in a situation with an infinite number of degrees of freedom. Since it solves the quantum constraints of general relativity it is also a candidate for a theory of quantum gravity. It is likely, however, that the solutions constructed correspond to a spurious sector of solutions of the constraints. The richness of the resulting theory makes it an interesting example to be analyzed by forthcoming techniques that construct the semiclassical limit of spin network quantum 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?
The physical states of the Gambini-Pullin model are, in a certain sense, solutions to various regularizations of the scalar constraint for Riemannian LQG.
“A remarkable feature is that the corresponding physical states are (in a certain sense) solutions to various regularizations of the scalar constraint for (Riemannian) LQG.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [193]
Gambini and Pullin introduced a very simple model obtained by modifying the BF theory skein relations.
“Gambini and Pullin [193] introduced a very simple model obtained by modification of the BF theory skein relations.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [193]
The definition of the Gambini-Pullin spin-foam model is not explicit because the theory is directly defined by the physical skein relations.
“The definition of this spin-foam model is not explicit since the theory is directly defined by the physical skein relations.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [193]
The Gambini-Pullin modification forbids some skein relations, which frees local excitations of a field theory.
“Gambini and Pullin define a model by modifying these amplitudes so that some of the skein relations are now forbidden. This simple modification frees local excitations of a field theory.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [193]
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
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/4/011 · Cited by 750 · see citing works
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/5/012 · Cited by 416 · 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
Differential geometry on the space of connections via graphs and projective limits
Ashtekar, A., & Lewandowski, J. (1995) · Journal of Geometry and Physics · doi:10.1016/0393-0440(95)00028-g · Cited by 303 · 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
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/5/010 · Cited by 170 · see citing works
Mazur, P. O., & Mottola, E. (1990) · Nuclear Physics B · doi:10.1016/0550-3213(90)90268-i · Cited by 165 · see citing works
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/5/011 · Cited by 128 · see citing works
Thiemann, T. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/6/005 · Cited by 89 · see citing works
LOOP CONSTRAINTS: A HABITAT AND THEIR ALGEBRA
LEWANDOWSKI, J., & MAROLF, D. (1998) · International Journal of Modern Physics D · doi:10.1142/s0218271898000231 · Cited by 76 · see citing works
Ooguri, H. (1992) · Nuclear Physics B · doi:10.1016/0550-3213(92)90188-h · Cited by 76 · see citing works
Perturbative Finiteness in Spin-Foam Quantum Gravity
Crane, L., Perez, A., & Rovelli, C. (2001) · Physical Review Letters · doi:10.1103/physrevlett.87.181301 · Cited by 64 · see citing works
Gaul, M., & Rovelli, C. (2001) · Classical and Quantum Gravity · doi:10.1088/0264-9381/18/9/301 · Cited by 56 · see citing works
Consistent Canonical Quantization of General Relativity in the Space of Vassiliev Invariants
Di Bartolo, C., Gambini, R., Griego, J., & Pullin, J. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.2314 · Cited by 37 · see citing works
Self-citationChern-Simons states in spin-network quantum gravity
Gambini, R., Griego, J., & Pullin, J. A. (1997) · Physics Letters B · doi:10.1016/s0370-2693(97)01048-4 · Cited by 27 · see citing works
Self-citationBartolo, C. D., Gambini, R., Griego, J., & Pullin, J. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/16/310 · Cited by 21 · see citing works
Self-citationA proposal for analysing the classical limit of kinematic loop gravity
Varadarajan, M., & Zapata, J. A. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/19/309 · Cited by 20 · see citing works
Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure
Bartolo, C. D., Gambini, R., Griego, J., & Pullin, J. (2000) · Classical and Quantum Gravity · doi:10.1088/0264-9381/17/16/309 · Cited by 17 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
Background independent quantum gravity: a status report
Ashtekar, A., & Lewandowski, J. (2004) · Classical and Quantum Gravity · doi:10.1088/0264-9381/21/15/r01 · Cited by 1,951 · 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
Group Field Theory: An overview
Freidel, L. (2005) · CERN Document Server (European Organization for Nuclear Research) · Cited by 249 · see citing works
The Phoenix Project: master constraint programme for loop quantum gravity
Thiemann, T. (2006) · Classical and Quantum Gravity · doi:10.1088/0264-9381/23/7/002 · Cited by 236 · see citing works
Bibliography 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
Noncommutative geometry induced by spin effects
Colatto, L. P., Penna, A. L. A., & dos Santos, W. C. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.105007 · Cited by 7 · see citing works
Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum GravityPreprint
D’Ambrosio, F. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.04651 · Cited by 3 · see citing works
Amplitudes in the Spin Foam Approach to Quantum Gravity
Chen, L.-Q. (2017) · UWSpace (University of Waterloo)
- Authors
- Gambini, R., & Pullin, J.
- Affiliations
- Universidad de la República de Uruguay (UY)
- Louisiana State University (US)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2002-07-15
- Volume
- 66
- Issue
- 2
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2049085852
- Cited by
- 10
- References
- 18
- Citations by year
- 2020: 1 · 2019: 1 · 2017: 1 · 2013: 1
- FWCI
- 0.83
- 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)
- Civil War Book Review (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
- spin foam models, quantum gravity, BF theory, spin network states, infinite degrees of freedom, three-dimensional quantum gravity, four-dimensional quantum gravity, semiclassical limit
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
