Jean Pierre GAZEAU
University Paris 7 Denis Diderot,
Boite 7020,
2 place Jussieu,
75251 Paris Cedex 05,

Coherent states quantization of simple systems

We present a general method of quantization based on families of coherent states or frames. Simple examples will be given, like the quantization of the motion on the circle, on 1+1 de Sitter space-time or on a discrete set of points. We shall also present new inequalities or spectral correlations resulting from such a quantization scheme for the particle motion in flat or curved geometries. For the quantum motion on the line, these inequalities concern the respective spectra of position operator and the momentum operator and are of  nature different of the usual Heisenberg inequalities.