Oscillator quantization of the massive scalar particle dynamics on AdS spacetime

Abstract

The set of trajectories for massive spinless particles on $Ad{S}_{N+1}$ 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 UIR's of SO(2,N) for generic $N$. The representations as usual can be characterized by their minimal energy $\alpha$ and are valid in the whole range of $\alpha$ allowed by unitarity.

arXiv commentLatex, 14 pages, version to appear in PLB

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• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• Coset construction of AdS particle dynamics
• Coordinate representation of particle dynamics in AdS and in generic static spacetimes
• Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$