Massless scalar particle on AdS spacetime: hamiltonian reduction and quantization

We investigate the massless scalar particle dynamics on AdSN+1 (N>1) by the method of Hamiltonian reduction. Using the dynamical integrals of the conformal symmetry we construct the physical phase space of the system as a SO(2,N+1) orbit in the space of symmetry generators. The symmetry generators themselves are represented in terms of (N+1)-dimensional oscillator variables. The physical phase space establishes a correspondence between the AdSN+1 null-geodesics and the dynamics at the boundary of AdSN+2. The quantum theory is described by a UIR of SO(2,N+1) obtained at the unitarity bound. This representation contains a pair of UIR's of the isometry subgroup SO(2,N) with the Casimir number corresponding to the Weyl invariant mass value. The whole discussion includes the globally well-defined realization of the conformal group via the conformal embedding of AdSN+1 in the ESU R x SN