ℏ-independent universality of the quantum and classical canonical transformations

Abstract

A theory of non-unitary-invertible and also unitary canonical transformations is formulated in the context of Weyl's phase space representations. It is shown in the phase space that all quantum canonical transformations without an explicit ℏ dependence are also classical mechanical and vice versa. Contrary to some earlier results, it is also shown that the quantum generators and their classical counterparts are identical in this ℏ-independent universal class.