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Other Representations

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

Abstract

The choice of representation is determined by the choice of polarization. The polarization spanned by the Hamiltonian vector fields of the position functions gives rise to the Schrödinger representation. The momentum representation corresponds to the polarization spanned by the Hamiltonian vector fields of the momentum variables. The Blattner-Kostant-Sternberg kernel between these representations reduces to the Fourier transform. In this chapter, we describe the Bargmann-Fock representation defined by the polarization spanned by the Hamiltonian vector fields of complex coordinates on the phase space as well as the harmonic oscillator energy representation.

Keywords

Phase Space Holomorphic Function Harmonic Oscillator Integral Manifold Momentum Variable 
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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