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Oscillator quantization of the massive scalar particle dynamics on AdS spacetime

Harald Dorn·George Jorjadze
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Abstract

The set of trajectories for massive spinless particles on $AdS_{N+1}$ 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 $α$ and are valid in the whole range of $α$ allowed by unitarity.

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Harald Dorn, George Jorjadze. 2005-08-17. Oscillator quantization of the massive scalar particle dynamics on AdS spacetime. https://doi.org/10.1016/j.physletb.2005.08.059

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