Quantizations from (P)OVM's
Quantum Physics
2015-06-17 v1 Mathematical Physics
math.MP
Abstract
We explain the powerful role that operator-valued measures can play in quantizing any set equipped with a measure, for instance a group (resp. group coset) with its invariant (resp. quasi-invariant) measure. Coherent state quantization is a particular case. Such integral quantizations are illustrated with two examples based on the Weyl-Heisenberg group and on the affine group respectively. An interesting application of the affine quantization in quantum cosmology is mentioned, and we sketch a construction of new coherent states for the hydrogen atom.
Cite
@article{arxiv.1310.3304,
title = {Quantizations from (P)OVM's},
author = {Hervé Bergeron and Evaldo M. F. Curado and Jean-Pierre Gazeau and Ligia M. C. S. Rodrigues},
journal= {arXiv preprint arXiv:1310.3304},
year = {2015}
}