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The localizability of particles in de Sitter space

Abstract Motivated by the Iwasawa decomposition and its geometrical interpretation, two new decompositions of the de Sitter group are obtained. The first is applied to construct the representations of the de Sitter group in a form immediately comparable with those of the Poincaré group. In particular they act on functions over an hyperboloid like the momentum hyperboloid of the Poincaré group, although they require both positive and negative mass shells of that hyperboloid. Using the second decomposition it is shown that the representations of the de Sitter group are localizable in the sense of Mackey and Wightman. Position operators are exhibited.