Fuzzy de Sitter space-times via coherent states quantization

J.-P. Gazeau , J. Mourad (1) , J. Queva (1)

1 APC (UMR_7164) - AstroParticule et Cosmologie

A construction of the 2d and 4d fuzzy de Sitter hyperboloids is carried out by using a (vector) coherent state quantization. We get a natural discretization of the dS "time" axis based on the spectrum of Casimir operators of the respective maximal compact subgroups SO(2) and SO(4) of the de Sitter groups SO_0(1,2) and SO_0(1,4). The continuous limit at infinite spins is examined.

Mots clés: Coherent states; quantization; non-commutative geometry; de Sitter space-time; Fuzzy manifolds

Domaines: Physique Quantique [quant-ph]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Relativité Générale et Cosmologie Quantique [gr-qc]

J.-P. Gazeau, J. Mourad, J. Queva. Fuzzy de Sitter space-times via coherent states quantization. XXVIth Colloquium on Group Theoretical Methods in Physics, Jun 2006, New-York, United States. pp.236-240. ⟨hal-00109968⟩