Continuum spin foam model for 3d gravity
Open accessAbstract
An example illustrating a continuum spin foam framework is presented. This covariant framework induces the kinematics of canonical loop quantization, and its dynamics is generated by a renormalized sum over colored polyhedra. Physically the example corresponds to 3d gravity with cosmological constant. Starting from a kinematical structure that accommodates local degrees of freedom and does not involve the choice of any background structure (e.g., triangulation), the dynamics reduces the field theory to have only global degrees of freedom. The result is projectively equivalent to the Turaev–Viro model.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
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?
Zapata formalized the idea of a continuum spin-foam description of 3-dimensional gravity using projective techniques inspired by the canonical picture.
“Recently, Zapata [372, 371] formalized the idea of a continuum spin-foam description of 3-dimensional gravity using projective techniques inspired by those utilized in the canonical picture [32].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [371]
Zapata constructs the continuum extension of the Turaev-Viro model for non-vanishing cosmological constant.
“Zapata concentrates on the case with non-vanishing cosmological constant and constructs the continuum extension of the Turaev-Viro model.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [371]
Cites
Ramanujan, M. S., & Schaefer, H. (1967) · American Mathematical Monthly · doi:10.2307/2316078 · Cited by 3,954 · 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
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
Relativistic Spin Networks and Quantum GravityPreprint
Barrett, J. W., Crane, L., & Crane, J. W. B. L. (1998) · Cited by 423 · see citing works
(1995) · CERN Document Server (European Organization for Nuclear Research) · Cited by 412 · 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
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
Baez, J. C. (1998) · Classical and Quantum Gravity · doi:10.1088/0264-9381/15/7/004 · Cited by 381 · see citing works
Temperley-Lieb recoupling theory and invariants of 3-manifolds
Kauffman, L. H., & LINS, S. L. S. (1994) · Cited by 377 · 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
Baez, J. C. (1996) · Advances in Mathematics · doi:10.1006/aima.1996.0012 · Cited by 266 · 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
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
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
Worldsheet formulations of gauge theories and gravityPreprint
Reisenberger, M. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9412035 · Cited by 60 · see citing works
Spin foam diagrammatics and topological invariance
Girelli, F., Oeckl, R., & Perez, A. (2002) · Classical and Quantum Gravity · doi:10.1088/0264-9381/19/6/305 · Cited by 39 · 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-citationPath integral for the loop representation of lattice gauge theories
Aroca, J. M., Fort, H., & Gambini, R. (1996) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.54.7751 · Cited by 9 · see citing works
Flagged first, then by citations
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
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
Noui, K., & Perez, A. (2005) · Classical and Quantum Gravity · doi:10.1088/0264-9381/22/9/017 · Cited by 181 · see citing works
Spin-foams for all loop quantum gravity
Kamiński, W., Kisielowski, M., & Lewandowski, J. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/9/095006 · Cited by 191 · see citing works
Spin foam quantization and anomalies
Bojowald, M., & Perez, A. (2010) · General Relativity and Gravitation · doi:10.1007/s10714-009-0892-9 · Cited by 35 · see citing works
- Authors
- Zapata, J. A.
- Affiliations
- Instituto de Matemáticas UNAM, Morelia Mich. 58090 México
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 2002-11-01
- Volume
- 43
- Issue
- 11
- Pages
- 5612-5623
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W2076480876
- Cited by
- 24
- References
- 18
- Citations by year
- 2016: 1 · 2015: 1 · 2014: 2 · 2013: 3 · 2012: 4
- FWCI
- 1.45
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Mathematical Physics (publishedVersion)
- arXiv (Cornell University) (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, three-dimensional gravity, cosmological constant, loop quantum gravity, renormalization, projective equivalence, background-independent 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
