New spinfoam vertex for quantum gravity
Open accessAbstract
We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the $15j$ symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints.
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The coherent intertwiner basis relevant for the definition of spin foams and the 4D quantum gravity amplitude was also derived by Livine and Speziale.
“The coherent intertwiner basis relevant for the definition of spin foams and the 4D quantum gravity amplitude was also derived by Livine and Speziale in [254].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [254]
Freidel and Krasnov introduced new four-dimensional gravity spin-foam models using the coherent state basis of the Livine-Speziale quantum tetrahedron.
“Freidel and Krasnov [182] introduced a set of new spin-foam models for four-dimensional gravity using the coherent state basis of the quantum tetrahedron of Livine and Speziale [254].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [254]
Spin-foam models are derived as quantizations of discretized classical theories.
“The SFMs on the other hand, are derived as quantizations of discretized classical theories [6, 13, 19, 20].”
From Spin-foams for all loop quantum gravity (2010) · cites this paper as [20]
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“Recently, a vertex amplitude that modifies the BC amplitude, and which addresses precisely the problems that we find here, has been proposed [16, 17 ], see also [18].”
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- Authors
- Livine, E. R., & Speziale, S.
- Affiliations
- École Normale Supérieure de Lyon (FR)
- ORCID
- Livine, Etera R.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2007-10-22
- Volume
- 76
- Issue
- 8
- ISSN
- 0556-2821 (ISSN-L)
- 1550-7998
- 1550-2368
- OpenAlex
- W2144853672
- Cited by
- 401
- References
- 45
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 16 · 2023: 10 · 2022: 7 · 2021: 44 · 2020: 16 · 2019: 15 · 2018: 25 · 2017: 8 · 2016: 16 · 2015: 13 · 2014: 19 · 2013: 41 · 2012: 33
- FWCI
- 20.32
- 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)
- HAL (submittedVersion)
- arXiv (Cornell University)
- Funders
- Government of Canada
- Institut Périmètre de physique théorique
- Natural Sciences and Engineering Research Council of Canada
- 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
- 4D quantum gravity, SU(2) coherent states, semiclassical states, quantum constraints, tetrahedral geometry, quantum correlations, loop quantum gravity
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