Classical motion of coloured test particles along geodesics of a Kaluza-Klein spacetime

Abstract

A general equation of classical particle motion is derived by projection of geodesics from a principal fibre bundle regarded as a Kaluza-Klein spacetime manifold. The high dimensional lifted metric is constructed from the Einstein’s gravity, from a non-Abelian Yang-Mills and from a scalar field. This Brans-Dicke type scalar field describes the possible variation of the metric on the gauge group among biinvariant ones. The equation of motion obtained here generalizes the well-known Wong equation and contains the force law in non-linear electrodynamical background field as a special case too. The particle’s charge is translated in parallel along the spacetime worldline. The mass of the moving particle varies and extra forces appear because of the presence of the scalar field. As an example we investigate the nonrelativistic motion of an electrically charged point mass in the field of the Dirac monopole. We find that the particle (even with zero angular momentum) cannot pass through the centre of the monopole, when it is treated in the Born-Infeld electrodynamics.