On three quantization methods for particle on hyperboloid

Details On three quantization methods for particle on hyperboloid On three quantization methods for particle on hyperboloid

2005-03-14

arxiv.org/abs/gr-qc/0503060v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, no figures, revtex

Scientific paper

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 demonstrate that standard technique for finding an irreducible representation within the geometric quantization scheme fails. For consistency we recall our earlier results concerning the other two methods, make some improvements and generalizations.

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