The Experts below are selected from a list of 306 Experts worldwide ranked by ideXlab platform
Benjamin Bahr - One of the best experts on this subject based on the ideXlab platform.
-
Hopf link volume simplicity constraints in spin foam models
Classical and Quantum Gravity, 2020Co-Authors: Mehdi Assanioussi, Benjamin BahrAbstract:In this article we consider specific Bivector geometries which arise in the large-spin limit of the extension of the Engle-Pereira-Rovelli-Livine spin foam model for quantum gravity by Kaminski, Kisielowski and Lewandowski. We address the implementation of volume simplicity constraints, which are required to ensure that a $4d$ metric can be reconstructed from the Bivector geometry. We find that the necessary conditions are closely related, but not quite equal to the Hopf link volume simplicity constraints introduced in earlier works. We estimate the number of independent geometricity conditions for arbitrary Bivector geometries, and find that they always agree with the number of Hopf links on the graph minus one, suggesting that the geometricity conditions can generically be formulated by deformation of the Hopf link volume simplicity constraints.
-
Volume of 4-polytopes from Bivectors
arXiv: General Relativity and Quantum Cosmology, 2018Co-Authors: Benjamin BahrAbstract:In this article we prove a formula for the volume of 4-dimensional polytopes, in terms of their face Bivectors, and the crossings within their boundary graph. This proves that the volume is an invariant of Bivector-coloured graphs in $S^3$.
Mehdi Assanioussi - One of the best experts on this subject based on the ideXlab platform.
-
Hopf link volume simplicity constraints in spin foam models
Classical and Quantum Gravity, 2020Co-Authors: Mehdi Assanioussi, Benjamin BahrAbstract:In this article we consider specific Bivector geometries which arise in the large-spin limit of the extension of the Engle-Pereira-Rovelli-Livine spin foam model for quantum gravity by Kaminski, Kisielowski and Lewandowski. We address the implementation of volume simplicity constraints, which are required to ensure that a $4d$ metric can be reconstructed from the Bivector geometry. We find that the necessary conditions are closely related, but not quite equal to the Hopf link volume simplicity constraints introduced in earlier works. We estimate the number of independent geometricity conditions for arbitrary Bivector geometries, and find that they always agree with the number of Hopf links on the graph minus one, suggesting that the geometricity conditions can generically be formulated by deformation of the Hopf link volume simplicity constraints.
Ahmed Zeglaoui - One of the best experts on this subject based on the ideXlab platform.
-
Warped Poisson Brackets on Warped Products
The Journal of Geometric Mechanics, 2014Co-Authors: Yacine Aït Amrane, Rafik Nasri, Ahmed ZeglaouiAbstract:In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure ([10]) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three Bivector fields on a product manifold and show that each of them lead under certain conditions to a Poisson structure. One of these Bivector fields will be called the warped Bivector field. For a warped product of pseudo-Riemannian manifolds equipped with a warped Bivector field, we compute the corresponding contravariant Levi-Civita connection and the curvatures associated with.
-
Warped Poisson Brackets on Warped Products
arXiv: Differential Geometry, 2013Co-Authors: Yacine Aït Amrane, Rafik Nasri, Ahmed ZeglaouiAbstract:In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three Bivector fields on a product manifold and show that each of them lead under certain conditions to a Poisson structure. One of these Bivector fields will be called the warped Bivector field. For a warped product of pseudo-Riemannian manifolds equipped with a warped Bivector field, we compute the corresponding contravariant Levi-Civita connection and the curvatures associated with.
-
Construction of Poisson tensors on warped product
2013Co-Authors: Rafik Nasri, Ahmed ZeglaouiAbstract:In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three Bivector fields on a product manifold and show that each of them lead under certain conditions to a Poisson structure. One of these Bivector fields will be called the warped Bivector field. For a warped product of pseudo-Riemannian manifolds equipped with a warped Bivector field, we compute the corresponding contravariant Levi-Civita connection and the curvatures associated with.
Sigbjørn Hervik - One of the best experts on this subject based on the ideXlab platform.
-
Higher dimensional Bivectors and classification of the Weyl operator
Classical and Quantum Gravity, 2009Co-Authors: Alan Coley, Sigbjørn HervikAbstract:We develop the Bivector formalism in higher dimensional Lorentzian spacetimes. We define the Weyl Bivector operator in a manner consistent with its boost-weight decomposition. We then algebraically classify the Weyl tensor, which gives rise to a refinement in dimensions higher than four of the usual alignment (boost-weight) classification, in terms of the irreducible representations of the spins. We are consequently able to define a number of new algebraically special cases. In particular, the classification in five dimensions is discussed in some detail. In addition, utilizing the (refined) algebraic classification, we are able to prove some interesting results when the Weyl tensor has (additional) symmetries.
F. Sommen - One of the best experts on this subject based on the ideXlab platform.
-
The problem of defining abstract Bivectors
Results in Mathematics, 1997Co-Authors: F. SommenAbstract:In this paper we investigate the problem of defining Bivectors on a purely abstract level. This leads to algebras of symbolic vectors and Bivectors.