Integral quantization: Weyl-Heisenberg versus affine group
Jean Pierre Gazeau (Université Paris Diderot)

After a few remarks about what we mean by quantization, I will explain the powerful role that operator-valued measure can play in quantizing any set equipped with a measure, for instance a group equipped with its (left) Haar measure. Integral quantizations based on the Weyl-Heisenberg group and on the affine group are compared. I will insist on the probabilistic aspects of such a procedure. An interesting application in quantum cosmology will be presented.