Spacetime metric and Yang–Mills fields unified in a Galilean subspace structure

Abstract

A novel approach to the unification of spacetime metric and Yang–Mills fields is presented. The spacetime metric field appears naturally as part of a first order G‐structure, a Galilean subspace structure on a world manifold of higher dimension. There is an a priori distinction between internal space dimensions and spacetime dimensions. The prolongation of the first order Galilean subspace structure to second order is a principal bundle of second order coframes which has additional degrees of freedom in the second order part of its gauge group. The Yang–Mills fields are defined in a natural way as second order gauge fields by a reduction of the second order Galilean subspace structure. The Yang–Mills fields appear as part of a connection on the world manifold rather than on the spacetime manifold. The kinematic foundations of the new model are analyzed using the theory of G‐structures and their prolongations. Kaluza–Klein models are also discussed from the G‐structure viewpoint and compared with the Galilean subspace model.