论文标题
扭转瓦利利的粒子动力学
Particle dynamics on torsional galilean spacetimes
论文作者
论文摘要
我们研究了伽利略型的均匀运动空间上的自由粒子运动。我们的分析中包括了三个众所周知的Galilei和（a）DS-Galilei空间的案例，但我们的重点将放在先前未开发的脉动脉动脉冲空间上。我们展示了在精选的坐标中如何与阻尼谐波振荡器的动力学相等，并通过扭转设置的阻尼。从保守的指控方面，运动对称代数的实现是微妙的，并带来了一些有趣的惊喜，例如Hamiltonian Vector Fields的同型版本和Poisson Bracket的相应概括。我们表明，Bargmann的扩展与所有Galilean运动学对称性是普遍的，但它不再是非零扭转的中心。我们还通过动力学的艾森哈特（Eisenhart）提升了这一事实的几何解释。
We study free particle motion on homogeneous kinematical spacetimes of galilean type. The three well-known cases of Galilei and (A)dS--Galilei spacetimes are included in our analysis, but our focus will be on the previously unexplored torsional galilean spacetimes. We show how in well-chosen coordinates free particle motion becomes equivalent to the dynamics of a damped harmonic oscillator, with the damping set by the torsion. The realization of the kinematical symmetry algebra in terms of conserved charges is subtle and comes with some interesting surprises, such as a homothetic version of hamiltonian vector fields and a corresponding generalization of the Poisson bracket. We show that the Bargmann extension is universal to all galilean kinematical symmetries, but also that it is no longer central for nonzero torsion. We also present a geometric interpretation of this fact through the Eisenhart lift of the dynamics.
