Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis (CROSBI ID 264398)
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Podaci o odgovornosti
Jurman, Danijel
engleski
Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
We consider the Lie group generated by the Lie algebra of kappa-Minkowski space. Imposing the invariance of the metric under the pull-back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with this group. This metric coincides with the metric of de Sitter space-time. We analyze the structure of unitary representations of the group which are relevant for the realization of the non-commutative κ- Minkowski space by embedding into (2D−1)- dimensional Heisenberg algebra. Using a suitable set of generalized coherent states, we select the particular Hilbert space and realize the non-commutative kappa-Minkowski space as an algebra of the Hilbert-Schmidt operators. We define dequantization map and fuzzy variant of the Laplace-Beltrami operator such that dequantization map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami operator on the half of de Sitter space-time.
fuzzy/non‐commutative de Sitter space ; kappa‐Minkowski space ; matrix geometry
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Podaci o izdanju
67 (4)
2019.
1800061
8
objavljeno
0015-8208
1521-3978
10.1002/prop.201800061