2017/10/31 by Danijel Jurman · 1 citation
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1002/prop.201800061
published as Fortsch.Phys. 67 (2019) 1800061 · 21 pages, v3 differs from version published in Fortschritte der Physik by a note and references added and adjusted
arxiv created 2019/09/23 · arxiv updated 2019/09/24
We consider the Lie group ℝDκ generated by the Lie algebra of κ-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 ℝDκ. This metric coincides with the metric of de Sitter space-time. We analyze the structure of unitary representations of the group ℝDκ 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 κ-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.