Oscillator quantization of the massive scalar particle dynamics on AdS spacetime

Details Oscillator quantization of the massive scalar particle dynamics on AdS spacetime Oscillator quantization of the massive scalar particle dynamics on AdS spacetime

2005-07-04

arxiv.org/abs/hep-th/0507031v2

Phys.Lett. B625 (2005) 117-126

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 14 pages, version to appear in PLB

Scientific paper

10.1016/j.physletb.2005.08.059

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 $\alpha$ and are valid in the whole range of $\alpha$ allowed by unitarity.

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