De Sitter Special Relativity

A special relativity based on the de Sitter group is introduced. Like ordinary special relativity, it retains the quotient character of spacetime, and consequently a notion of homogeneity. This means that the underlying spacetime will be a de Sitter spacetime, the quotient space between de Sitter and the Lorentz groups. Since the local symmetry will also be given by the de Sitter group, each tangent space must be replaced by an osculating de Sitter spacetime. As far as the de Sitter group can be considered a particular deformation of the Poincaré group, this theory turns out to be a specific kind of deformed special relativity. The modified notions of energy and momentum are obtained, and the exact relationship between them explicitly exhibited. The causal structure of spacetime, which is modified by the presence of the de Sitter length parameter, is briefly discussed.