Fermion dynamics in the Kaluza-Klein monopole geometry

Abstract

The behaviour of charged particles in the Kaluza-Klein monopole geometry is studied. A discussion of the five-dimensional geodesics is followed by an analysis of the corresponding Dirac equation. A main observation is that a charged particle cannot reach the core of the pole, in contrast with the conventional case. For the Dirac particle this comes about because the dimensional reduction generates a radius dependent anomalous magnetic moment which asymptotically yields a gyromagnetic ratio g = 1. This has the following consequences: (i) there is no Lipkin-Weisberger-Peshkin problem in the lowest angular momentum channel, (ii) there are no bound states, (iii) scattering leads to helicity-flip rather than to charge-exchange which would be another logical possibility. Our results indicate that there is no phenomenon, analogous to the Rubakov-Callan effect to be expected for the Kaluza-Klein monopole.