Snyder's Quantized Space-time and De Sitter Special Relativity

Abstract

There is a one-to-one correspondence between Snyder's model in de Sitter space of momenta and the \dS-invariant special relativity. This indicates that physics at the Planck length $\ell_P$ and the scale $R=3/\Lambda$ should be dual to each other and there is in-between gravity of local \dS-invariance characterized by a dimensionless coupling constant $g=\ell_P/R\sim 10^{-61}$.