Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim

TL;DR

This paper introduces a Hamilton-Jacobi formalism for analyzing test particles in 5D brane-world models, showing that both mass and charge can vary over time due to large extra dimensions, affecting fundamental constants.

Contribution

It proposes a clear, invariant method to define and analyze variable mass and charge in 5D theories, improving upon geodesic approaches and incorporating electromagnetic fields.

Findings

Effective rest mass varies with extra dimension

Electric charge of particles changes along trajectories

Cosmological variations of fundamental constants are demonstrated

Abstract

In classical Kaluza-Klein theory, with compactified extra dimensions and without scalar field, the rest mass as well as the electric charge of test particles are constants of motion. We show that in the case of a large extra dimension this is no longer so. We propose the Hamilton-Jacobi formalism, instead of the geodesic equation, for the study of test particles moving in a five-dimensional background metric. This formalism has a number of advantages: (i) it provides a clear and invariant definition of rest mass, without the ambiguities associated with the choice of the parameters used along the motion in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the discussion, and (iii) we avoid the difficulties associated with the "splitting" of the geodesic equation. For particles moving in a general 5D metric, we show how the effective rest mass, as measured by an observer in 4D, varies as a consequence of the large extra dimension. Also, the fifth component of the momentum changes along the motion. This component can be identified with the electric charge of test particles. With this interpretation, both the rest mass and the charge vary along the trajectory. The constant of motion is now a combination of these quantities. We study the cosmological variations of charge and rest mass in a five-dimensional bulk metric which is used to embed the standard k = 0 FRW universes. The time variations in the fine structure "constant" and the Thomson cross section are also discussed.