Generalized spinfoams
Open accessAbstract
We reconsider the spinfoam dynamics that has been recently introduced, in the generalized Kami\ifmmode \acute{n}\else \'{n}\fi{}ski-Kisielowski-Lewandowski (KKL) version where the foam is not dual to a triangulation. We study the Euclidean as well as the Lorentzian case. We show that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex. This constraint implies that boundary states admit a (quantum) geometrical interpretation in terms of polyhedra, generalizing the tetrahedral geometry of the simplicial case. We also point out that the general solution to this constraint (imposed weakly) depends on a quantum number ${r}_{f}$ in addition to those of loop quantum gravity. We compute the vertex amplitude and recover the KKL amplitude in the Euclidean theory when ${r}_{f}=0$. We comment on the eventual physical relevance of ${r}_{f}$, and the formal way to eliminate it.
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For a given j, the allowed values are k = j − r for all half-integers r such that k > 0.
“In particular, given j, one has k = j − r for all possible half-integers such that k > 0 [140].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [140]
The EPRL amplitudes can be generalized to arbitrary complexes with boundaries given by graphs with nodes of arbitrary valence.
“as in BF theory, the EPRL amplitudes can be generalized to arbitrary complexes with boundaries given by graphs with nodes of arbitrary valence. The extension of the model to arbitrary complexes was first studied in [237, 236] and has been revisited in [140].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [140]
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- Authors
- Ding, Y., Han, M., & Rovelli, C.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- ORCID
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2011-06-09
- Volume
- 83
- Issue
- 12
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W3037467603
- Cited by
- 60
- References
- 70
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 1 · 2023: 1 · 2022: 2 · 2021: 6 · 2020: 2 · 2019: 4 · 2018: 4 · 2017: 3 · 2016: 2 · 2015: 2 · 2014: 2 · 2013: 10 · 2012: 10
- FWCI
- 7.02
- 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)
- 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
- simplicity constraints, vertex amplitude, loop 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 ›
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