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Symplectic Group, Quantum Mechanics and Anosov’s Systems

  • André Avez
Part of the International Centre for Mechanical Sciences book series (CISM, volume 261)

Abstract

Dirac’s canonical quantization is studied in the general framework of symplectic Mechanics. Existence and uniqueness of such a quantization are investigated. Particular attention is paid to R2n: in particular it is proved that there is only one canonical quantization which recovers the usual spectrum of the harmonic oscillator.

Keywords

Harmonic Oscillator Poisson Bracket Symplectic Manifold Jacobi Identity Symplectic Group 
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Copyright information

© Springer-Verlag Wien 1980

Authors and Affiliations

  • André Avez
    • 1
  1. 1.Département de MécaniqueUniversité Paris VIParisFrance

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