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

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.