Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-07-04
Physics
High Energy Physics
High Energy Physics - Theory
15 pages. Invited talk given at `International workshop on noncommutative geometry and physics', Beijing, Nov. 7-10, 2005. To
Scientific paper
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 $R\simeq(3\Lambda^{-1})^{1/2}$, which is another fundamental length related to the cosmological constant. Here, the cosmological constant $\Lambda$ 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 $g= \sqrt{3} \ell_P/R\simeq(G\hbar c^{-3}\Lambda)^{1/2}\sim 10^{-61}$.
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