Fuzzy de Sitter space-times via coherent states quantization
Jean-Pierre Gazeau (APC), Jihad Mourad (APC), Julien Queva (APC)
TL;DR
This paper constructs fuzzy de Sitter space-times in 2D and 4D using coherent state quantization, leading to a natural discretization of the time axis and analyzing the continuous limit at infinite spins.
Contribution
It introduces a novel method to discretize de Sitter space-times via coherent states, connecting the spectrum of Casimir operators to the space-time structure.
Findings
Discretization of de Sitter time axis based on Casimir spectra
Construction of 2D and 4D fuzzy de Sitter hyperboloids
Analysis of the continuous limit at infinite spins
Abstract
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.
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Taxonomy
TopicsMathematical Analysis and Transform Methods