On canonical transformations and quantization rules

Abstract

We find that only linear and point canonical transformations are quantized into quantum canonical transformations. This result does not depend on the quantization procedure. We examine quantization rule invariance under linear and point canonical transformations and show that it holds only for special classes of phase-space functions. However, Weyl’s rule (and only this rule) is found to be invariant under linear canonical transformations forall phase-space functions.