Group theory and nonlinear phenomena in physics

物理学中的群论和非线性现象

• 批准号: RGPIN-2016-04025
• 负责人: Winternitz, Pavel
• 金额: $ 2.91万
• 依托单位: Université de Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=633063
• 关键词: Group; theory; nonlinear; phenomena; physics

Superintegrable systems are Hamiltonian systems that allow more integrals of motion than they have degrees of freedom. The best known ones and only rotationally invariant ones are the harmonic oscillator and the Kepler-Coulomb system. They are of physical interest for several reasons. They are exactly solvable . The integrals of motion form interesting non-Abelian algebras. In classical mechanics all bounded trajectories in maximally superintegrable systems are closed and the motion is periodic. In quantum mechanics they exhibit "accidental" degeneracy of energy levels. Until recently superintegrable systems were considered to be extremely rare. Recently we have

超可积系统是允许运动积分多于自由度的哈密顿系统。最著名的和唯一的旋转不变的是谐振子和开普勒-库仑系统。 它们具有物理意义有几个原因。它们是完全可解的。运动积分构成有趣的非阿贝尔代数。在经典力学中，极大超可积系统的所有有界轨线都是封闭的，并且运动是周期的。在量子力学中，它们表现出能级的“偶然”简并。直到最近，超可积系统被认为是极其罕见的。最近我们