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The Beltrami Model of De Sitter Space: From Snyder's quantized space-time to de Sitter invariant relativity

Han-Ying Guo
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Abstract

In terms of the Beltrami model of de Sitter space we show that there is an interchangeable relation between Snyder's quantized space-time model in dS-space of momenta at the Planck length $\ell_P=(G\hbar c^{-3})^{1/2}$ and the dS-invariant special relativity in dS-spacetime of radius $R\simeq(3Λ^{-1})^{1/2}$, which is another fundamental length related to the cosmological constant. Here, the cosmological constant $Λ$ is regarded as a fundamental constant together with the speed of light $c$, Newton constant $G$ and Planck constant $\hbar$. Furthermore, the physics at two fundamental scales of length, the \dS-radius $R$ and the Planck length $\ell_P$, should be dual to each other and linked via the gravity with local dS-invariance characterized by a dimensionless coupling constant $g= \sqrt{3} \ell_P/R\simeq(G\hbar c^{-3}Λ)^{1/2}\sim 10^{-61}$.

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Han-Ying Guo. 2006-07-04. The Beltrami Model of De Sitter Space: From Snyder's quantized space-time to de Sitter invariant relativity. https://arxiv.org/abs/hep-th/0607017

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