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On three quantization methods for particle on hyperboloid
J.-P. Gazeau1, M. Lachièze-Rey1, W. Piechocki

We compare the respective efficiencies of three quantization methods (group theoretical, coherent state and geometric) by quantizing the dynamics of a free massive particle in two-dimensional de Sitter space. For each case we consider the realization of the principal series representation of $SO_0(1,2)$ group and its two-fold covering SU(1,1). We obtain the 'no go theorem' for finding an irreducible representation within the geometric quantization scheme. For consistency we recall our earlier results concerning the other two methods, make some improvements and generalizations.
1 :  APC - UMR 7164 - AstroParticule et Cosmologie
Physique/Relativité Générale et Cosmologie Quantique
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