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.KeywordsLine BundleRepresentation SpacePoisson AlgebraComplex Line BundleHamiltonian Vector FieldThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.