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

TL;DR

This paper uses higher-dimensional gravity theories to derive collisional stopping power, linking extra-dimensional physics with transport phenomena and recovering classical results under certain conditions.

Contribution

It introduces a novel approach using Kaluza-Klein theory and compactification to analytically determine stopping power, bridging higher-dimensional field theory with transport phenomena.

Findings

Recovering Bethe-Møller formula in large R limit

Model supports anisotropic and nonlinear medium responses

Framework can be matched to experimental data with a normalization constant

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.