Quantization of AdS × S particle in static gauge

We quantize the particle dynamics in AdSN+1 × SM spacetime in static gauge, which leads to the coordinate representation with wavefunctions depending only on spatial coordinates. The energy square operator is quadratic in canonical momenta and contains a scalar curvature term. We analyze the self-adjointness of this operator and calculate its spectrum. We then construct unitary representations of the isometry group SO(2, N) × SO(M + 1) and calculate the quantum relation between the Casimir numbers. (paper)