International Journal of Theoretical Physics

, Volume 16, Issue 8, pp 615–633 | Cite as

On representation spaces in geometric quantization

  • Jedrzej Śniatycki
  • Stanley Toporowski


The structure of the space of wave functions in the representation given by a complete strongly admissible polarization of the phase space is investigated. The conditions that the wave functions should be covariant constant along the real part of the polarization define the Bohr-Sommerfeld set of the representation containing the supports of all wave functions. There is a natural scalar product for the wave functions defined on the Bohr-Sommerfeld set. It is shown, for a real polarization, that the resulting Hilbert space of wave functions is not trivial if and only if the Bohr-Sommerfeld set is not empty.


Wave Function Hilbert Space Field Theory Phase Space Elementary Particle 
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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • Jedrzej Śniatycki
    • 1
  • Stanley Toporowski
    • 1
  1. 1.Department of Mathematics and StatisticsThe University of CalgaryCalgaryCanada

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