Coherent states quantization of simple systems
Abstract:
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.