Hamiltonian formulation of the 5-D Kaluza-Klein model and test-particle motion

TL;DR

This paper reformulates the 5-D Kaluza-Klein model using the ADM approach, linking gauge fields to gravitational variables, analyzing particle motion, and revealing a potential variation in the fine structure constant due to an extra scalar field.

Contribution

It provides a Hamiltonian formulation of the 5-D Kaluza-Klein model that preserves dimensional reduction and clarifies the relation between gauge fields and gravitational variables.

Findings

Time component of gauge vector linked to gravitational multipliers

Charge definition recovered in reduced electrodynamics

Identification of a scalar field causing a varying fine structure constant

Abstract

We examine the ADM reformulation of the 5-D KK model: the dimensional reduction is provided to commute with the ADM splitting and we show how the time component of the gauge vector is given by combination of the Lagrangian multipliers for the 5-D gravitational field. We consider 5D particles motion and after dimensional reduction the definition of charge is recovered within electrodynamic coupling. A time-varying fine structure constant is recognized because an extra scalar field is present in the 4-D theory.