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Andrzej Sitarz - One of the best experts on this subject based on the ideXlab platform.
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Star product realizations of kappa-Minkowski Space
Journal of Noncommutative Geometry, 2013Co-Authors: Bergfinnur Durhuus, Andrzej SitarzAbstract:We define a family of star products and involutions associated with $\kappa$-Minkowski Space. Applying corresponding quantization maps we show that these star products restricted to a certain Space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products it is demonstrated that they can be extended to a class of polynomially bounded smooth functions allowing a realization of the full Hopf algebra structure on $\kappa$-Minkowski Space. Furthermore, we give an explicit realization of the action of the $\kappa$-Poincar\'e algebra as an involutive Hopf algebra on this representation of $\kappa$-Minkowski Space and initiate a study of its properties.
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Noncommutative Differential Calculus on the Kappa-Minkowski Space
Physics Letters B, 1995Co-Authors: Andrzej SitarzAbstract:Following the construction of the $\kappa$-Minkowski Space from the bicrossproduct structure of the $\kappa$-Poincare group, we investigate possible differential calculi on this noncommutative Space. We discuss then the action of the Lorentz quantum algebra and prove that there are no 4D bicovariant differential calculi, which are Lorentz covariant. We show, however, that there exist a five-dimensional differential calculus, which satisfies both requirements. We study also a toy example of 2D $\kappa$-Minkowski Space and and we briefly discuss the main properties of its differential calculi.
Kumar S. Gupta - One of the best experts on this subject based on the ideXlab platform.
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Kappa-Minkowski Space-time and the star product realizations
The European Physical Journal C, 2007Co-Authors: Stjepan Meljanac, A. Samsarov, Marko Stojic, Kumar S. GuptaAbstract:We investigate a Lie algebra-type $ \kappa$-deformed Minkowski Space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $ \kappa$-Minkowski Space. The coproduct and the star product corresponding to each of them are found. Utilizing the properties of the {\em{natural}} realization, we construct a scalar field theory on $ \kappa$-deformed Minkowski Space and show that it is equivalent to the scalar, nonlocal, relativistically invariant field theory on the ordinary Minkowski Space.
Nie Zhi - One of the best experts on this subject based on the ideXlab platform.
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SUBMANIFOLDS IN Minkowski Space WITH CONSTANT SUPPORT FUNCTION
Journal of Mathematics, 2004Co-Authors: Nie ZhiAbstract:A complete connected submanifold with constant support function is a Finsler sphere or a plane are given in the Minkowski Space. Two kinds of submanifols are studied by using support function.The result is a popularized result in the Euclidean Space, and corresponding result is optimized in it.
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On Submanifolds of Minkowski Space
Journal of Mathematical Research and Exposition, 2002Co-Authors: Nie ZhiAbstract:Submanifolds flag curvature and Ricci curvature of submanifolds is studied by using normal curvature, Landsberg Curvature, normal tangent Curvature, Berwald connection, and second fundamenal form in Minkowski Space.
M. Tahiri - One of the best experts on this subject based on the ideXlab platform.
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Note on quantum Minkowski Space
Physical Review D, 2008Co-Authors: Z. Bentalha, M. TahiriAbstract:In this work, some interesting details about quantum Minkowski Space and quantum Lorentz group structures are revealed. The task is accomplished by generalizing an approach adopted in a previous work where quantum rotation group and quantum Euclidean Space structures have been investigated. The generalized method is based on a mapping relating the q-spinors (precisely the tensor product of dotted and undotted fondamental q-spinors) to Minkowski q-vectors. As a result of this mapping, the quantum analog of Minkowski Space is constructed (with a definite metric). Also, the matrix representation of the quantum Lorentz group is determined together with its corresponding q-deformed orthogonality relation.
Chen Xin-yue - One of the best experts on this subject based on the ideXlab platform.
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SOME PROPERTIES OF SUBMANIFOLDS IN A Minkowski Space
Journal of Mathematics, 2000Co-Authors: Chen Xin-yueAbstract:In this paper we study submanifolds in a Finsler manifold. In particular,we give a characteristic of hyperspheres in a Minkowski Space. Meanwhile,we discuss the second fundamental form of the hypersurfaces in a Minkowski Space.