Canonical-quantization for classical dynamic Neuman-type systems in frames of the Moser spectral approach
The classical Neumann type dynamical systems describe the motion of a particles constrained to live on an $N$-sphere $S^N$ in $(N+l)$-dimensional space $\mathbb{R}^{N+1}$ and submitted to quasi-harmonic forces. Following the Moser spectral approach to a connection of the infinite dimensional finite-...
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8123 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | The classical Neumann type dynamical systems describe the motion of a particles constrained to live on an $N$-sphere $S^N$ in $(N+l)$-dimensional space $\mathbb{R}^{N+1}$ and submitted to quasi-harmonic forces. Following the Moser spectral approach to a connection of the infinite dimensional finite-zoned by Lax dynamical systems with the finite dimensional Neumann type systems on sphere in $\mathbb{R}^{N+1}$, the regular procedure to quantize of them suitably is supposed. The quantum expression of the commuting conserved currents for the quantum Neumann type dynamical systems are determined in a general case via the Dirac canonical quantization procedure. |
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