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Introduction

  • Jȩdrzej Śniatycki
Chapter
  • 382 Downloads
Part of the Applied Mathematical Sciences book series (AMS, volume 30)

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.

Keywords

Line Bundle Representation Space Poisson Algebra Complex Line Bundle Hamiltonian Vector Field 
These 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.

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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Jȩdrzej Śniatycki
    • 1
  1. 1.The University of CalgaryCalgaryCanada

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