Jurman, Danijel (2019) Fuzzy de Sitter Space from kappaMinkowski Space in Matrix Basis. Fortschritte der Physik, 67 (4). pp. 18. ISSN 00158208

PDF
 Accepted Version
 article
Download (215kB)  Preview 
Abstract
We consider the Lie group generated by the Lie algebra of kappaMinkowski space. Imposing the invariance of the metric under the pullback 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 spacetime. We analyze the structure of unitary representations of the group which are relevant for the realization of the noncommutative 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 noncommutative kappaMinkowski space as an algebra of the HilbertSchmidt operators. We define dequantization map and fuzzy variant of the LaplaceBeltrami operator such that dequantization map relates fuzzy eigenvectors with the eigenfunctions of the LaplaceBeltrami operator on the half of de Sitter spacetime.
Item Type:  Article  

Uncontrolled Keywords:  fuzzy/non‐commutative de Sitter space ; kappa‐Minkowski space ; matrix geometry  
Subjects:  NATURAL SCIENCES > Mathematics > Geometry and Topology NATURAL SCIENCES > Physics > General and Classical Physics NATURAL SCIENCES > Physics > Physics of Elementary Particles and Fields 

Divisions:  Theoretical Physics Division  
Projects: 


Depositing User:  Danijel Jurman  
Date Deposited:  14 Dec 2020 09:53  
URI:  http://fulir.irb.hr/id/eprint/6125  
DOI:  10.1002/prop.201800061 
Actions (login required)
View Item 