Operator spin foam models
Open accessAbstract
The goal of this paper is to introduce a systematic approach to spin foams. We define operator spin foams, that is foams labelled by group representations and operators, as the main tool. An equivalence relation we impose in the set of the operator spin foams allows to split the faces and the edges of the foams. The consistency with that relation requires introduction of the (familiar for the BF theory) face amplitude. The operator spin foam models are defined quite generally. Imposing a maximal symmetry leads to a family we call natural operator spin foam models. This symmetry, combined with demanding consistency with splitting the edges, determines a complete characterization of a general natural model. It can be obtained by applying arbitrary (quantum) constraints on an arbitrary BF spin foam model. In particular, imposing suitable constraints on Spin(4) BF spin foam model is exactly the way we tend to view 4d quantum gravity, starting with the BC model and continuing with the EPRL or FK models. That makes our framework directly applicable to those models. Specifically, our operator spin foam framework can be translated into the language of spin foams and partition functions. We discuss the examples: BF spin foam model, the BC model, and the model obtained by application of our framework to the EPRL intertwiners.
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A consistent modification of the EPRL model can be obtained by replacing the non-projector object with a genuine projector.
“As proposed in [49, 235] one can obtain a consistent modification of the EPRL model by replacing (167) by a genuine projector , graphically 168”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [49]
The requirement of anomaly freedom under the discrete symmetry can be met by suitable definitions of the transition amplitudes.
“We have seen that this requirement (advocated in [90]) can be met by suitable definitions of the transition amplitudes [49, 235]”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [49]
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- Authors
- Bahr, B., Hellmann, F., Kamiński, W., Kisielowski, M., & Lewandowski, J.
- Affiliations
- University of Warsaw (PL)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2011-04-06
- Volume
- 28
- Issue
- 10
- Pages
- 105003
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2142641312
- Cited by
- 63
- References
- 62
- Citations by year
- 2025: 1 · 2024: 1 · 2022: 1 · 2021: 1 · 2020: 2 · 2019: 4 · 2018: 3 · 2017: 3 · 2016: 4 · 2015: 1 · 2014: 12 · 2013: 10 · 2012: 14
- FWCI
- 9.92
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- Trinity's Access to Research Output (TARA) (Trinity College Dublin) (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, EPRL model, 4D quantum gravity, intertwiners, partition function, group representations
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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