Gauge Model Based on Group G×SU(2)

We present a model of gauge theory based on the symmetry group G×SU(2) where G is the gravitational gauge group and SU(2) is the internal group of
symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form with spherical symmetry. The solution for the gravitational potentials induces a metric of Schwarzschild type on the gravitational gauge group space.