Unified gravitational and Yang-Mills fields

We unify the gravitational and Yang-Mills fields by extending the diffeomorphisms in (N=4+n)-dimensional space-time to a larger group, called the conservation group. This is the largest group of coordinate transformations under which conservation laws are covariant statements. We present two theories that are invariant under the conservation group. Both theories have field equations that imply the validity of Einstein's equations for general relativity with the stress-energy tensor of a non-Abelian Yang-Mills field (with massive quanta) and associated currents. Both provide a geometrical foundation for string theory and admit solutions that describe the direct product of a compactn-dimensional space and flat four-dimensional space-time. One of the theories requires that the cosmological constant shall vanish. The conservation group symmetry is so large that there is reason to believe the theories are finite or renormalizable.