Quantizations from (P)OVM's

8th International Symposium on Quantum Theory and Symmetries

Bergeron, H.^1 ; Curado, E.M.F.^2,3 ; Gazeau, J.P.^2,4 ; Rodrigues, Ligia M. C. S.^2

Univ Paris-Sud, ISMO, UMR 8214, 91405 Orsay, France^1

Centro Brasileiro de Pesquisas Fisicas, Brazil^2

Instituto Nacional de Ciencia e Tecnologia - Sistemas Complexos, Rua Xavier Sigaud 150, 22290-180 - Rio de Janeiro, RJ, Brazil^3

APC, UMR 7164, Univ Paris Diderot, Sorbonne Paris Cité, 75205 Paris, France^4

关键词: Affine groups;    Coherent state;    Heisenberg group;    Hydrogen atoms;    Quantum cosmology;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012032/pdf
DOI  :  10.1088/1742-6596/512/1/012032

来源: IOP

【 摘 要 】

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.