论文标题
Koopman-Von Neumann力学的Eisenhart举重
Eisenhart lift of Koopman-von Neumann mechanics
论文作者
论文摘要
艾森哈特（Eisenhart）的升力在非权利主义和相对论物理学之间建立了有趣的联系，从而提供了对非偏见主义牛顿力学的时空几何理解。然而，鲜为人知的是，经典力学（也称为Koopman-von Neumann Mechanics）的希尔伯特空间表示，试图使经典力学与量子力学相同的数学结构。在本文中，我们使用Eisenhart Toolkit几何将Koopman-von Newmann（KVN）力学化。然后，我们使用KVN力学的几何视图来找到在KVN力学背景下与谐波振荡器，线性电势和自由粒子相关的转换。
The Eisenhart lift establishes a fascinating connection between non-relativistic and relativistic physics, providing a space-time geometric understanding of non-relativistic Newtonian mechanics. What is still little known, however, is the fact that there is a Hilbert space representation of classical mechanics (also called Koopman-von Neumann mechanics) that attempts to give classical mechanics the same mathematical structure that quantum mechanics has. In this article, we geometrize the Koopman-von Newmann (KvN) mechanics using the Eisenhart toolkit. We then use a geometric view of KvN mechanics to find transformations that relate the harmonic oscillator, linear potential, and free particle in the context of KvN mechanics.
