Massless scalar particle on AdS spacetime: hamiltonian reduction and quantization

We investigate the massless scalar particle dynamics on $AdS_{N+1} ~ (N>1)$by the method of Hamiltonian reduction. Using the dynamical integrals of theconformal 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 generatorsthemselves are represented in terms of $(N+1)$-dimensional oscillatorvariables. The physical phase space establishes a correspondence between the$AdS_{N+1}$ null-geodesics and the dynamics at the boundary of $AdS_{N+2}$. Thequantum theory is described by a UIR of $SO(2,N+1)$ obtained at the unitaritybound. This representation contains a pair of UIR's of the isometry subgroupSO(2,N) with the Casimir number corresponding to the Weyl invariant mass value.The whole discussion includes the globally well-defined realization of theconformal group via the conformal embedding of $AdS_{N+1}$ in the ESU$\rr\times S^N$.Comment: 14 pages, Late