Kaluza-Klein Theory as a Dynamics in a Dual Geometry

TL;DR

This paper explores how the dynamics of relativistic systems can be represented as geodesic flows on a dual manifold, revealing a Kaluza-Klein geometric structure when electromagnetic interactions are included.

Contribution

It demonstrates that the dual geometric space of relativistic systems naturally exhibits Kaluza-Klein structure, linking Hamiltonian dynamics with higher-dimensional geometry.

Findings

Geodesic flow describes orbits of non-relativistic Hamiltonian systems.

Introduction of electromagnetic interaction induces Kaluza-Klein geometry.

Dual space geometry reflects electromagnetic effects in relativistic systems.

Abstract

It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flow on a manifold and an associated dual. This method can be applied to a four dimensional manifold of orbits in space-time associated with a relativistic system. One can study the consequences on the geometry of the introduction of electromagnetic interaction. We find that resulting geometrical structure in the dual space is that of Kaluza and Klein.