MASSIVE SPINNING PARTICLE ON ANTI-DESITTER SPACE

To describe a massive particle with fixed, but arbitrary, spin on d = 4 anti-de Sitter space M(4), we propose the point particle model with configuration space M(6) = M(4) x S-2, where the sphere S-2 correspond s to the spin degrees of freedom. The model possesses two gauge symmet ries expressing strong conservation of the phase space counterparts of the second and fourth order Casimir operators for so(3,2). We prove t hat the requirement of energy to have a global positive minimum E(o) o ver the configuration space is equivalent to the relation E(o) > s, s being the particle's spin, which presents the classical counterpart of the quantum massive condition. States with minimal energy are studied in detail. The model is shown to be exactly solvable. It can be strai ghtforwardly generalized to describe a spinning particle on d-dimensio nal anti-de Sitter space M(d), with M(2(d-1)) = Md x S-(d-2) the corre sponding configuration space.