Massless scalar particle on AdS spacetime: Hamiltonian reduction and quantization

Abstract

We investigate the massless scalar particle dynamics on $Ad{S}_{N+1}(N>1)$ 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 $Ad{S}_{N+1}$ null-geodesics and the dynamics at the boundary of $Ad{S}_{N+2}$. 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 $Ad{S}_{N+1}$ in the ESU $\rr\times S^N$.

arXiv comment14 pages, Latex

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• On the propagator of a scalar field in AdS x S and in its plane wave limit
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