A fibre bundle description of coupled gravitational and gauge fields

Abstract

This article can be understood as a preamble to consider principal fibre bundles associated to gauge fields as a true arena for physical fields and particles. The bundle approach to gauge fields and the generalized Kaluza-Klein theory are reviewed. Physically plausible conditions imposed on the metric tensor on the bundle imply restrictions on admissible gauge groups, formulated here as necessary and sufficient conditions. Geodesics on the bundle are shown to describe motion of classical particles with non-Abelian gauge charge. An attempt to give for a linear connection on the bundle a role independent on the metric structure leads to averting the principal difficulty of the generalized Kaluza-Klein theory: presence of an enormous cosmological constant.

Based on a lecture delivered at the Conference on Differential Geometrical Methods in Mathematical Physics, Salamanca 1979.

Alexander von Humboldt fellow