Oscillator quantization of the massive scalar particle dynamics on AdS spacetime

The set of trajectories for massive spinless particles on AdSN+1 spacetime is described by the dynamical integrals related to the isometry group SO(2,N). The space of dynamical integrals is mapped one to one to the phase space of the N-dimensional oscillator. Quantizing the system canonically, the classical expressions for the symmetry generators are deformed in a consistent way to preserve the so(2,N) commutation relations. This quantization thus yields new explicit realizations of the spin zero positive energy UIRs of SO(2,N) for generic N. The representations as usual can be characterized by their minimal energy α and are valid in the whole range of α allowed by unitarity.