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arXiv · 1310.3304

Quantizations from (P)OVM's

Hervé Bergeron·Evaldo M. F. Curado·Jean-Pierre Gazeau·Ligia M. C. S. Rodrigues
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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.

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Hervé Bergeron, Evaldo M. F. Curado, Jean-Pierre Gazeau, Ligia M. C. S. Rodrigues. 2013-10-11. Quantizations from (P)OVM's. https://doi.org/10.1088/1742-6596/512/1/012032

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