Covariant fields on anti-de Sitter spacetimes

Abstract

The covariant free fields of any spin on anti-de Sitter spacetimes are studied, pointing out that these transform under isometries according to covariant representations of the anti-de Sitter isometry group, induced by those of the Lorentz group. Applying the method of ladder operators it is shown that the covariant representations with unique spin are equivalent with discrete unitary irreducible representations of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations may depend on the mass and spin of the covariant field. The conclusion is that on anti-de Sitter spacetime one cannot formulate an universal mass condition as in special relativity.