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

Publisher Website
Google Scholar
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.