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Classical dynamics from a unitary representation of the Galilei group
Annals of Physics ( IF 3 ) Pub Date : 2020-05-01 , DOI: 10.1016/j.aop.2020.168157
A.D. Bermúdez Manjarres , M. Nowakowski , D. Batic

We give a formulation of classical mechanics in the language of operators acting on a Hilbert space. The formulation given comes from a unitary irreducible representation of the Galilei group that is compatible with the basic postulates of classical mechanics, particularly the absence of an uncertainty principle between the position and momentum of a particle. It is shown that the theory exposed in the article contains the Koopman-von Neumann formalism of classical mechanics as a particular case.

中文翻译:

从伽利莱群的单一表示的经典动力学

我们用作用于希尔伯特空间的算子的语言给出了经典力学的表述。给出的公式来自伽利略群的单一不可约表示,它与经典力学的基本假设兼容,特别是在粒子的位置和动量之间不存在不确定性原理。结果表明,文章中公开的理论包含经典力学的库普曼-冯诺依曼形式主义作为一个特例。
更新日期:2020-05-01
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