Quantizations from (P)OVM's

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.

References in corpus (2)

• Integral quantizations with two basic examples
• A Note on Distribution Spaces on Manifolds

Cited by in corpus (4)

• Affine quantisation of the Brans-Dicke theory: Smooth bouncing and the equivalence between the Einstein and Jordan frames
• POVM Quantization
• Ambiguous power spectrum from a quantum bounce
• Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light