Projector on physical states in loop quantum gravity
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We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism-invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like, spacetime formalism for quantum gravity and relates this theory to the spin foam models. We also discuss how expectation values of the physical quantity can be computed.
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The construction was generalized to four dimensions by Crane and Yetter, giving a discrete topological field theory corresponding in the continuum to BF theory and an invariant of 4-manifolds.
“This construction was generalized to the four-dimensional case by Crane and Yetter [25,26], giving a discrete topological field theory corresponding in the continuum to BF theory [57] and an invariant of 4-manifolds.”
From Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity (2001) · cites this paper as [26]
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The fermionic contribution to the spectrum of the area operator in nonperturbative quantum gravity
Montesinos, M., & Carlo Rovelli, C. (1998) · CERN Document Server (European Organization for Nuclear Research) · Cited by 5 · see citing works
Baez, J. C. (2003) · Contemporary mathematics - American Mathematical Society · doi:10.1090/conm/318/05541 · Cited by 5 · see citing works
String theory in a vertex operator representation: a simple model for testing loop quantum gravityPreprint
Starodubtsev, A. N. (2002) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/0201089 · 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
Loop Quantum Gravity: an introduction
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Relating spin foams and canonical quantum gravity: (n−1)+1 formulation of nD spin foams
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Topological methods in quantum gravity
Starodubtsev, A. N. (2005) · UWSpace (University of Waterloo) · Cited by 4 · 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
Quantum Cauchy surfaces in canonical quantum gravity
Lin, C.-Y. (2016) · Classical and Quantum Gravity · doi:10.1088/0264-9381/33/18/185009 · Cited by 2 · see citing works
Emergence of general relativity from loop quantum gravity: a summary
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Emergence of scalar matter from spin foam model
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Quantum reference frames via transition amplitudes in timeless quantum gravity
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Spin Foam Models of Gravity and BF Theory as evolution of Spin NetworksPreprint
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On some aspects of canonical and covariant approaches to quantum gravity
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Quantum General Invariance and Loop Gravity
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Complete loop quantum gravity graviton propagator
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Quantum Dynamics in Loop Quantum Gravity
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- Authors
- Rovelli, C.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1999-04-22
- Volume
- 59
- Issue
- 10
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2070533344
- Cited by
- 95
- References
- 56
- Citations by year
- 2026: 1 · 2024: 2 · 2023: 1 · 2022: 1 · 2021: 1 · 2020: 1 · 2019: 3 · 2018: 3 · 2017: 3 · 2016: 3 · 2015: 3 · 2014: 5 · 2013: 4 · 2012: 2
- FWCI
- 5.40
- 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)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Centre National de la Recherche Scientifique
- 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
- loop quantum gravity, physical states, projection operators, diffeomorphism invariance, path integral, spin foam models, quantum gravity, expectation values
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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.
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