汉密尔顿力学的雅可比群对称性

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-06-11 DOI:10.1016/j.geomphys.2024.105249

Stephen G. Low, Rutwig Campoamor-Stursberg

引用次数: 0

摘要

我们证明，一个具有时间、能量、动量和位置自由度的扩展相空间的差分变形，在位置-动量子空间上留下不变的交点 2 形和退化的正交度量 dt2（对应于牛顿时间线元素），局部满足汉密尔顿方程，直到位置-动量子空间上的通常典型变换为止。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Jacobi group symmetry of Hamilton's mechanics

We show that diffeomorphisms of an extended phase space with time, energy, momentum and position degrees of freedom leaving invariant a symplectic 2-form and a degenerate orthogonal metric $d t^{2}$ , corresponding to the Newtonian time line element, locally satisfy Hamilton's equations up to the usual canonical transformation on the position-momentum subspace.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity