Principal bundles and gauge theories in the space-time \(\mathbb R \times S^ 3\) (Q1373697)

The author describes gauge theories on a principal fibre bundle \(P(M,G,\pi)\) with \(M=\mathbb R\times S^3\) as the base manifold and \(G\) as the structural group. If \(G\) is an internal group of symmetry, he obtains the Yang-Mills gauge theories. If \(G\) is the Lorentz or Poincaré group, the gauge theory implies the existence of a gravitational field. Finally, if \(M\) is endowed with a pseudo-Riemannian metric and \(G\) is an internal group of symmetries, the author obtains a unified theory of gravitation and gauge fields.