带电粒子在磁场和一般电场中运动的Noether对称性

Exact trajectories of charged particles in the Dirac monopole field

We consider the motion of charged particles in the presence of a Dirac magnetic monopole. We use an extension of Noether's theorem for systems with magnetic forces and integrate explicitly the equations of motion.

具有Lie和Noether点对称性的自治三维牛顿系统

Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries

确定了具有Lie点对称性的三维自治Newton系统和具有Noether点对称性的三维自治Newton Hamilton系统。我们应用的结果，以确定二维哈密顿动力系统，在一个空间中的常数非零曲率和可积通过Noether点对称。结果的推导是几何的，可以自然地扩展到更高的维度。

Symmetries of the dynamics and Noether theorem in classical mechanics

The aim of this note is to discuss the relation between one-parameter continuous symmetries of the dynamics, defined on physical grounds, and conservation laws. In the Hamiltonian formulation, such symmetries of the dynamics in general leave the Hamiltonian invariant only up to a total derivative $ d G(q)/d t$ . In this more general case, the corresponding formulation of Noether theorem gives that the conservation law displays a sort of ano\-ma\-ly, the constant of motion being the sum of the canonical generator of the symmetry transformations plus the generator $G$ of the gauge transformation…

含时 Hamilton-Lagrange 系统的 Noether 定理与 Lie 对称性

Noether's theorem and Lie symmetries for time-dependent Hamilton-Lagrange systems

本文回顾了含时 Hamilton 系统基于点变换的 Noether 和 Lie 对称性分析，阐明辅助方程关系并在更广泛势能类中发现不变量，以含时 Kepler 系统为例证明对称变换与不变量间无唯一关联。

Noether currents of locally equivalent symmetries

Local symmetry transformations play an important role for establishing the existence and form of a conserved (Noether) current in systems with a global continuous symmetry. We explain how this fact leads to the existence of linear relations between Noether currents of distinct global symmetries that coincide on the local level, thus generalizing the well-known relationship $\vec L=\vec r\times\vec p$ between momentum $\vec p$ and angular momentum $\vec L$. As a byproduct, we find a natural interpretation for the discrepancy between the canonical and metric energy-momentum tensors in theories o…

A geometric approach to the generalized Noether theorem

We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented in \cite{zhang2020generalized}. Our version of the generalized Noether theorem has several positive features: it is constructed in the most natural extension of the phase space, allowing for the symmetries to be vector fields on such manifold and for the associated invariants to be first integrals of motion; it has a direct geometrical proof, paralleling the proof of the standard phase space version of Noether's theorem; it automatically yields an inverse Noether theorem; it applies al…