Alexander V. Mikhailov教授学术报告

发布时间:2024-04-02 阅读量:

报告题目:Quantisation Ideals-a novel approach to the old problem of quantisation

报告人:  Alexander V. Mikhailov教授

工作单位: 英国利兹大学教授



报告摘要:We propose to revisit the problem of quantisation and look at it from an entirely new angle, focusing on the quantisation of dynamical systems themselves, rather than of their Poisson structures. We begin with a dynamical system defined on a free associative algebra generated by non-commutative dynamical variables and reduce the problem of quantisation to the problem of studying two-sided quantisation ideals. The multiplication rules in the quantum algebra  are manifestly associative and consistent with the dynamics. We found first examples of bi-quantum systems which are quantum counterparts of bi-Hamiltonian systems in the classical theory. Moreover, the new approach enables us to define and present first examples of non-deformation quantisations of dynamical systems, i.e. quantum systems that cannot be obtained as deformations of a classical dynamical system with commutative variables. In order to apply the novel approach to a classical system we need firstly lift it to a system on a free algebra preserving the most valuable properties, such as symmetries, conservation laws, or Lax integrability. The new approach sheds light on the long-standing problem of operator's ordering. We will use the well-known Volterra hierarchy and stationary KdV equations to illustrate the methodology.

报告人简介:Alexander V. Mikhailov,英国利兹大学数学学院教授。从事可积系统的研究活动,特别是可积系统、非对易可积系统分类和量子化问题。1978年在朗道理论物理研究所获得理论和数学物理博士学位,1987年全博士学位。剑桥大学克莱尔·霍尔学院终身院士。组织了多个会议和研讨会,并在国际期刊上发表了100多篇论文,引用次数超过3400次。