Spin foam diagrammatics and topological invariance
Open accessAbstract
We provide a simple proof of the topological invariance of the Turaev–Viro model (corresponding to simplicial 3D pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, proposed as models of quantum gravity in 4D, under refinement of the cellular decomposition.
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BF amplitudes are independent of the regulating triangulation, and with suitable regularization of bubble divergences the BF partition function is topologically invariant and discretization independent.
“using this graphical notation one can easily prove the discretization independence of the BF amplitudes.”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [206]
Equation (248) has been proven for simplicial decompositions, and its generalization to arbitrary cellular decomposition was obtained.
“Eq. (248) has been proven in this case for the case of simplicial decompositions in [364]; see also [363, 238]. The generalization for arbitrary cellular decomposition was obtained in [206].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [206]
The amplitudes of this spin-foam model are independent of the chosen cellular decomposition.
“The crucial property of this spin-foam model is that the amplitudes are independent of the chosen cellular decomposition [363, 206].”
From The Spin-Foam Approach to Quantum Gravity (2013) · cites this paper as [206]
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Research works printed but not linked: 1
- Zapata J A 2001 On the Turaev-Viro model and covariant loop quantization presented at the Workshop on Cannonical and Quantum Gravity III (Warsaw, 2001)
Cited by
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The Spin-Foam Approach to Quantum Gravity
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- Authors
- Girelli, F., Oeckl, R., & Perez, A.
- Affiliations
- Centre de Physique Théorique (FR)
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 2002-02-26
- Volume
- 19
- Issue
- 6
- Pages
- 1093-1108
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2013935989
- Cited by
- 39
- References
- 25
- Citations by year
- 2025: 1 · 2024: 1 · 2022: 1 · 2021: 1 · 2020: 2 · 2019: 1 · 2014: 1 · 2013: 1 · 2012: 2
- FWCI
- 3.52
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Classical and Quantum Gravity (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- topological invariance, state sum models, cosmological constant, cellular decomposition, quantum groups, quantum gravity
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