Internal geometrical structures on Minkowski space-time and Yang-Mills symmetries

Abstract

Yang-Mills potentials and fields on Minkowski space-time are equivalent to connections and curvatures for corresponding principle fibre bundles over Minkowski space-time. Therefore, the usual Yang-Mills field equations, together with Bianchi's identities, define transport equations for the connection and curvature with respect to a given observer field (inertial system). This equivalence is worked out; furthermore, the notion of symmetric, particularly spherically symmetric Yang-Mills connections is transposed to the bundle description. We show that the restrictions on the Yang-Mills connection imposed by spherical symmetry are by no means as severe as assumed by Ikeda and Miyachi.