标题： 通过Kaluza-Klein理论确定碰撞停止功率 显示英文标题

标题： On the Determination of Collisional Stopping Power via Kaluza-Klein Theory

摘要： 在本工作中，使用广义相对论的工具来解析推导碰撞停止功率。 我们从一个受卡鲁扎-克莱因启发的五维微分同胚不变作用量出发，在紧化后得到一个四维有效理论，在该理论中物质场被当作膜定位处理。 投影电子对介质的响应通过拉格朗日导出的相互作用以协变方式耦合到电磁和费米部分的对称张量场中。 当$R_c \sim \Lambda_{\text{EM}}^{-1}$、$\Lambda_{\text{EM}} \gg m_e$和$g_4^2 = \frac{3\pi^2 m_e v}{4\gamma^3 R_c^2 e^2 \Lambda_{\text{EM}}}$得到满足时，在大$R'$极限下显示出恢复了贝特-莫勒公式的主导项。 这里提出的构造可能作为一种替代方法，利用紧化几何和介质激发来确定可观测的耦合和停止功率。 该模型固有地支持与各向异性及非线性响应相关的现象，以及通过研究停止功率和粒子范围在实验室尺度系统中出现的引力或额外维度效应。 显示英文摘要

摘要： In this work, the tools of general relativity are used to analytically derive collisional stopping power. We start from a Kaluza-Klein inspired, five-dimensional diffeomorphism-invariant action, and upon compactification, obtain a four-dimensional effective theory in which the matter fields are treated to be brane-localized. The medium response to the projected electron is encoded in symmetric tensor fields coupled covariantly to both electromagnetic and fermionic parts via Lagrangian-derived interactions. When $R_c \sim \Lambda_{\text{EM}}^{-1}$, $\Lambda_{\text{EM}} \gg m_e$ and $g_4^2 = \frac{3\pi^2 m_e v}{4\gamma^3 R_c^2 e^2 \Lambda_{\text{EM}}}$ are satisfied, the leading term of Bethe-Moller formula is shown to be recovered in the large $R'$ limit. The construction presented here may serve as an alternative approach that uses compactification geometry and medium excitations to determine observable couplings and stopping power. The model intrinsically supports phenomena linked to anisotropy and nonlinear response, as well as gravitational or extra-dimensional effects in laboratory-scale systems via the study of stopping power and particle range.