On three quantization methods for particle on hyperboloid

Jean-Pierre Gazeau; Marc Lachieze-Rey; Wlodzimierz Piechocki

On three quantization methods for particle on hyperboloid

广义相对论与量子宇宙学 2007-05-23 v3 天体物理学高能物理 - 理论量子物理

作者: Jean-Pierre Gazeau , Marc Lachieze-Rey , Wlodzimierz Piechocki

摘要

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.

关键词

canonical quantization quantum state space quantum algebra

引用

@article{arxiv.gr-qc/0503060,
  title  = {On three quantization methods for particle on hyperboloid},
  author = {Jean-Pierre Gazeau and Marc Lachieze-Rey and Wlodzimierz Piechocki},
  journal= {arXiv preprint arXiv:gr-qc/0503060},
  year   = {2007}
}

备注

22 pages, no figures, revtex

On three quantization methods for particle on hyperboloid

摘要

关键词

引用

备注

相关论文