Coherent states and quantization of the particle motion on the line, on the circle, on 1 + 1-de Sitter space-time and of more general systems

We describe a quantization procedure based on adapted coherent states. This scheme could reveal itself as an efficient tool for quantizing physical systems for which more traditional methods are uneasy to implement. The procedure is illustrated by simple examples like the wellknown quantization of the particle motion on the line and the yet problematic quantization of the particle motion on the circle. Related to the latter problem is the quantization of dynamics of a test particle in two-dimensional de Sitter space, the group of symmetry of which is SO0(1, 2). The realization, along our quantization procedure, of the corresponding principal series representation of SO0(1, 2) seems to be a new result. We shall also present some extensions of the method to more elaborate mathematical structures : quantization of Grassmann structures by using Daoud-Kibler coherent states; coherent-state approach to the fuzzy sphere; Ashtekar polymer particle representation.