Dynamical Symmetry of the Kaluza-Klein Monopole

Abstract

One of the oldest and most enduring ideas regarding the unification of gravitation and gauge theory is Kaluza’s five dimensional unified theory. Kaluza’s hypothesis was that the world has four spatial dimensions, but one of the dimensions has curled up to form a circle so small as to be unobservable. He showed that ordinary general relativity in five dimensions, assuming such a cylindrical ground state, contained a local U(1) gauge symmetry arising from the isometry of the hidden fifth dimension. The extra components of the metric tensor constitutes the gague fields of this symmetry and could be identified with the electromagnetic vector potential.