On the von Neumann rule in quantization

Abstract

We show that any linear quantization map into the space of self-adjoint operators in a Hilbert space violates the von Neumann rule on post-composition with real functions.Comment: 12 pages. The second version changes only the division into chapters and adds a consideration of a related Experiment, the third one restructures the order of the theorems and adds some explanations and references. Theorems and proofs remain unchanged since the first versio