The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Combinatorial Space from Loop Quantum Gravity
Open accessAbstract
The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills fields (with or without fermions) coupled to gravity. It is argued that the operators induced by classical diffeomorphism invariant or covariant functions are respectively invariant or covariant under a suitable completion of the diffeomorphism group. The canonical quantization in terms of loop variables described here, yields a representation of the algebra of observables in a separable Hilbert space. Furthermore, the resulting quantum theory is equivalent to a model for diffeomorphism invariant gauge theories which replaces space with a manifestly combinatorial object.
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“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]
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Cites
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Loop space representation of quantum general relativity
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Real Ashtekar variables for Lorentzian signature space-times
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Black Hole Entropy from Loop Quantum Gravity
Rovelli, C. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.3288 · Cited by 660
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
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Gambini, R., Pullin, J., & Ashtekar, A. (1996) · doi:10.1017/cbo9780511524431 · Cited by 295
Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
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Research works printed but not linked: 10
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- Lewandowski, J., and Marolf, D. (1997). e-Print Archive: gr-qc/9710016 · arXiv
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- Anandan, J. (1981). Proc. Conf. Differential Geometric Methods in Physics (Trieste 1981) eds. G. Denardo, et al. (World Scientific, Singapore)
- Ashtekar, A., and Lewandowski, J. (1993). In Quantum Gravity and Knots, ed. J. Baez (Oxford University Press, Oxford).
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Cited by
(1998) · doi:10.12942/lrr-1998-1 · Cited by 917
Rovelli, C. (2017) · The Frontiers Collection · doi:10.1007/978-3-319-55420-4_10 · Cited by 299
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
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
Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit
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Metadata
- 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
- www.springernature.com/gp/researchers/text-and-data-mining (tdm)
- www.springernature.com/gp/researchers/text-and-data-mining (vor)
- www.springer.com/tdm (unspecified)
- 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 › Nuclear and High Energy 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
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
