Quantizations from (P)OVM's

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 illustrate...

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Bibliographic Details
Published in:Journal of physics. Conference series 2014-05, Vol.512 (1), p.12032-11
Main Authors: Bergeron, H, Curado, E M F, Gazeau, J P, Rodrigues, Ligia M C S
Format: Article
Language:English
Subjects:
Affine transformations
Coherence
Cosmology
Counting
Hydrogen atoms
Integrals
Invariants
Measurement
Operators (mathematics)
Physics
Quantization
Sketches
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Summary: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.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/512/1/012032