2019
Том 71
№ 11

All Issues

Reduction and geometric quantization

Mikityuk I. V., Prykarpatsky A. K.

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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.

English version (Springer): Ukrainian Mathematical Journal 44 (1992), no. 9, pp 1116-1122.

Citation Example: Mikityuk I. V., Prykarpatsky A. K. Reduction and geometric quantization // Ukr. Mat. Zh. - 1992. - 44, № 9. - pp. 1220–1228.

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