Quantization in complex symmetric spaces
Izvestiya. Mathematics , Tome 9 (1975) no. 2, pp. 341-379
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By means of the method described in the author's paper “Quantization” (Izv. Akad. Nauk SSSR Ser. Mat. 38 (1974), 1116–1174), we construct the quantization of a classical mechanics whose phase space is a classical complex symmetric space. We establish the important qualitative differences between the quantization of such mechanics and the quantization of ordinary mechanics with plane phase spaces: for all the spaces considered, except for the sphere, Planck's constant is bounded above. Moreover, in the compact case Planck's constant takes on only discrete values.
Bibliography: 17 items.
@article{IM2_1975_9_2_a6,
author = {F. A. Berezin},
title = {Quantization in complex symmetric spaces},
journal = {Izvestiya. Mathematics },
pages = {341--379},
publisher = {mathdoc},
volume = {9},
number = {2},
year = {1975},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_2_a6/}
}
F. A. Berezin. Quantization in complex symmetric spaces. Izvestiya. Mathematics , Tome 9 (1975) no. 2, pp. 341-379. http://geodesic.mathdoc.fr/item/IM2_1975_9_2_a6/