Canonical-quantization for classical dynamic Neuman-type systems in frames of the Moser spectral approach

  • М. М. (jr.), Bogoliubov Steclov Math. Inst., Moscow
  • I. V. Mykytiuk Inst. appl. probl. mech. and math., Lviv
  • В. M. Fil' Politechn. Inst., Lviv
  • A. К. Prykarpatsky Inst. appl. probl. mech. and math., Lviv
Keywords: -

Abstract

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.

References

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Published
03.08.1992
How to Cite
Bogoliubov М. М. (., Mykytiuk I. V., Fil’В. M., and Prykarpatsky A. К. “Canonical-Quantization for Classical Dynamic Neuman-Type Systems in Frames of the Moser Spectral Approach”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 44, no. 7, Aug. 1992, pp. 913-22, https://umj.imath.kiev.ua/index.php/umj/article/view/8123.
Section
Research articles