Email this article POLYNOMIAL QUANTIZTION AND OVERALGEBRA FOR HYPERBOLOID OF ONE SHEET
- Authors: Molchanov V.F.1
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Affiliations:
- Tambov State University named after G.R. Derzhavin
- Issue: Vol 23, No 123 (2018)
- Pages: 353-360
- Section: Articles
- URL: https://journals.rcsi.science/2686-9667/article/view/297239
- DOI: https://doi.org/10.20310/1810-0198-2018-23-123-353-360
- ID: 297239
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Abstract
We show that the multiplication of symbols in polynomial quantization is exactly an action of an overalgebra on the space of these symbols
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In [1] we constructed quantization in the spirit of Berezin on para-Hermitian symmetric spaces G/H , see also [2]. In [3] we showed that this quantization, anyway polynomial quantization - the most algebraic variant of quantization, can be considered as a part of the representation theory. In present paper we continue our activity in this direction, namely, we show that the multiplication of symbols is exactly an action of an overalgebra on the space of symbols, see Theorem 2. Here we restrict ourselves to a hyperboloid of one sheet in R3 . Besides, we write explicit formulae of this action.×
About the authors
Vladimir Fedorovich Molchanov
Tambov State University named after G.R. Derzhavin
Email: v.molchanov@bk.ru
Doctor of Physics and Mathematics, Professor of the Functional Analysis Department 33 Internatsionalnaya St., Tambov 392000, Russian Federation
References
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- Molchanov V.F. Berezin quantization as a part of the representation theory // Вестник Тамбовского университета. Серия Естественные и технические науки. Тамбов, 2017. Т. 22. Вып. 6. С. 1235-1246. doi: 10.20310/1810-0198-2017-22-6-1235-1246.
- Неретин Ю.А. Действие надалгебры в планшерелевском разложении и операторы сдвига в мнимом направлении // Известия РАН. Серия математическая. 2002. Т. 66. № 5. С. 171-182.
- Molchanov V.F. Canonical representations and overgroups // Amer. Math. Soc. Transl., Ser. 2. 2003. Vol. 210. P. 213-224.
- Molchanov V.F. Canonical representations for hyperboloids: an interaction with an overalgebra // Geometric Methods in Physics. Bialowieza, 2016. P. 129-138.
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