Introduction

Abstract

A classical system is described by the Poisson algebra of functions on the phase space of the system. Quantization associates to each classical system a Hilbert space V of quantum states and defines a map Q from a subset of the Poisson algebra to the space of symmetric operators on V. The domain of Q consists of all “Q-quantizable” functions. The definition of Q requires some additional structure on the phase space. The functions which generate one-parameter groups of canonical transformations preserving this additional structure are Q-quantizable. They form a subalgebra of the Poisson algebra satisfying

where [f₁, f₂] denotes the Poisson bracket of f₁, and f₂.