发表机构
Ludwig-Maximilians-Universität München; Technische Universität München; Boğaziçi University（慕尼黑大学; 慕尼黑工业大学; 博阿齐奇大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过拉格朗日 Euler-Poincare 约化，将庞加莱群上的自由相对论性自旋粒子类比为重陀螺，揭示时空位置为平流物理量，并阐明电磁场导致部分约化及左平凡化坐标对相互作用拉格朗日量的几何选择机制。
AI 中文摘要
重陀螺是半直积群上 Euler-Poincare 约化的经典例子，展示了平流物理量——重力方向——如何与旋转运动耦合。尽管通过李群构型描述相对论性自旋粒子在哈密顿（辛）力学中已得到充分确立，我们证明显式的拉格朗日 Euler-Poincare 约化提供了与重陀螺直接、透明的类比。具体而言，我们表明庞加莱群上的自由相对论性自旋粒子正是该系统的精确洛伦兹类比，其中时空位置是平流物理量。这种几何统一不仅阐明了两个系统背后的对称性，还解释了为何引入外部电磁场会导致部分约化。最后，我们确定向左平凡化坐标的过渡充当几何选择机制，自然偏向一类相互作用拉格朗日量，其中自旋-场耦合表现为粒子质量的动力学重新定义。
英文摘要
The heavy top is a classic example of Euler-Poincare reduction on a semidirect product group, demonstrating how an advected quantity-the direction of gravity-couples to rotational motion. While the description of relativistic spinning particles via Lie group configurations is well established in Hamiltonian (symplectic) mechanics, we demonstrate that an explicit Lagrangian Euler-Poincare reduction provides a direct, transparent parallel to the heavy top. Specifically, we show that the free relativistic spinning particle on the Poincare group is the precise Lorentzian analog of this system, with spacetime position being the advected quantity. This geometric unification not only illuminates the underlying symmetry of both systems but also clarifies why the introduction of external electromagnetic fields leads to a partial reduction. Finally, we establish that the transition to left-trivialized coordinates acts as a geometric selection mechanism, naturally favoring a class of interaction Lagrangians where spin-field coupling manifests as a dynamical redefinition of the particle's mass.
Comments13 pages
