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Reduction and geometric quantization

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Abstract

A construction is created that makes it possible to geometrically quantize a reduced Hamiltonian system using the procedure of geometric quantization realized for a Hamiltonian system with symmetries (i.e., to find the discrete spectrum and the corresponding eigenfunctions, if these have been found for the initial system). The construction is used to geometrically quantize a system obtained by reduction of a Hamiltonian system that determines the geodesic flow on an n-dimensional sphere.

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Additional information

Translated from Ukrayins'kyy Matematychnyy Zhurnal, Vol. 44, No. 9, pp. 1220–1228, September, 1992.

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Mykytyuk, I.V., Prykarpats'kyy, A.K. Reduction and geometric quantization. Ukr Math J 44, 1116–1122 (1992). https://doi.org/10.1007/BF01058372

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Keywords

  • Hamiltonian System
  • Discrete Spectrum
  • Initial System
  • Geometric Quantization
  • Geodesic Flow