Abstract

In this work we study integrability aspects of the current algebra representation and the factorized quantum nonlinear Schrödinger type dynamical systems, initiated before by G. Goldin with collaborators, in suitably renormalized Fock type Hilbert spaces. There is developed the current algebra representation scheme of reconstructing algebraically factorized quantum Hamiltonian and symmetry operators in the Fock type space. There is presented its application to constructing quantum factorized Hamiltonian systems and their symmetry operators in case of quantum integrable spatially many- and one-dimensional dynamical systems. As examples we have studied in detail the factorized structure of Hamiltonian operators, describing such quantum integrable spatially one-dimensional models as the Calogero–Moser–Sutherland and Nonlinear Schrödinger dynamical systems of spin-less Bose-particles.

中文翻译：

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当前代数表示和因式分解量子非线性Schrödinger型动力系统的可集成性方面

摘要

在这项工作中，我们研究了目前的代数表示形式和因式量子非线性Schrödinger型动力学系统的可积性方面，该动力学系统是由G. Goldin之前与合作者共同发起的，在适当地重新规范化的Fock型Hilbert空间中。开发了在Fock类型空间中重构代数分解量子哈密顿量和对称算子的当前代数表示方案。提出了在量子可积分空间多维和一维动力学系统的情况下构造量子分解哈密顿系统及其对称算子的应用。作为示例，我们详细研究了哈密顿算子的因式分解结构，