发表机构
Universidade Federal da Paraíba; Federal University of Campina Grande（帕拉伊巴联邦大学; 坎皮纳格兰德联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究不可积Weyl几何中Perlick固有时间的极值化，推导广义Euler-Lagrange方程，发现极值曲线与自平行线不同，具有非局域性，并在双重极限下涌现局域洛伦兹力动力学。
AI 中文摘要
我们研究了在不可积Weyl几何中Perlick固有时间的极值化问题。我们推导了相应的广义Euler--Lagrange方程，并表明所得的极值曲线通常不与Weyl联络的自平行线重合，它们的差异由Weyl长度曲率控制，并在可积情形下消失。极值方程的一个显著特征是其非局域性：在Weyl固有时间参数化下，加速度显式依赖于变分区间终点剩余的固有时间。我们针对弱常数Weyl场说明了这一行为，并表明在双重缩放极限下会出现局域洛伦兹力动力学，其中Weyl场趋于零且终端固有时间发散，而它们的乘积保持有限。这些结果揭示了固有时间极值化、Weyl不可积性与局域力动力学之间的非平凡关系。
英文摘要
We investigate the extremization of Perlick's proper time in non-integrable Weyl geometry. We derive the corresponding generalized Euler--Lagrange equations and show that the resulting extremals do not, in general, coincide with the autoparallels of the Weyl connection, their difference being governed by the Weyl length curvature and vanishing in the integrable case. A distinctive feature of the extremal equation is its nonlocal character: in the Weyl proper-time parametrization, the acceleration depends explicitly on the remaining proper time to the endpoint of the variational interval. We illustrate this behavior for a weak constant Weyl field and show that a local Lorentz-force dynamics emerges in a double-scaling limit in which the Weyl field vanishes and the terminal proper time diverges while their product remains finite. These results uncover a nontrivial relation between proper-time extremization, Weyl non-integrability, and local force dynamics.
Comments14 pages, 2 figures
