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

Abstract

In this work, the tools of general relativity are used to analytically derive collisional stopping power and a linkage between higher-dimensional field theory and transport phenomena is proposed. 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-M{\o}ller 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. The construction is gauge invariant, behaves consistently under limiting conditions, and can be matched to experimental stopping data through a single effective normalization constant.