论文标题
Volterra层次结构的量化
Quantisations of the Volterra hierarchy
论文作者
论文摘要
在本文中，我们探讨了基于定量理想概念的最近出现的定量问题方法。我们明确地证明了非亚伯伏尔特拉与其对称性的整个层次结构一起承认了变形定量。我们表明，Volterra层次结构的所有奇数对称性也承认也是非证明定量的。我们讨论了周期性伏特拉层次结构的定量问题，包括其量子哈密顿量，定量代数的中心要素，并证明了获得的量子系统的超积极性。我们表明，具有$ 3 $的Volterra系统承认了双量子结构，该结构可被视为其经典的双 - 汉密尔顿结构的量子变形。
In this paper we explore a recently emerged approach to the problem of quantisation based on the notion of quantisation ideals. We explicitly prove that the nonabelian Volterra together with the whole hierarchy of its symmetries admit a deformation quantisation. We show that all odd-degree symmetries of the Volterra hierarchy admit also a non-deformation quantisation. We discuss the quantisation problem for periodic Volterra hierarchy including their quantum Hamiltonians, central elements of the quantised algebras, and demonstrate super-integrability of the quantum systems obtained. We show that the Volterra system with period $3$ admits a bi-quantum structure, which can be regarded as a quantum deformation of its classical bi-Hamiltonian structure.
