Geodesic equations for a charged particle in the unified theory of gravitational and electromagnetic interactions

A new model of gravitational and electromagnetic interactions is constructed as a version of the classical Kaluza–Klein theory based on a five-dimensional manifold as the physical space–time. The velocity space of moving particles in the model remains four-dimensional as in the standard relativity theory. The spaces of particle velocities constitute a four-dimensional distribution over a smooth five-dimensional manifold. This distribution depends only on the electromagnetic field and is independent of the metric tensor field. We prove that the equations for the geodesics whose velocity vectors always belong to this distribution are the same as the charged particle equations of motion in the general relativity theory. The gauge transformations are interpreted in geometric terms as a particular form of coordinate transformations on the five-dimensional manifold.