Connections and Generalized Gauge Transformations

Elimination of the fibre coordinate dependence from the connection form transformation rule for a bundle with a coset manifold standard fibre reduces the structure group. The nonlinear SU(4) action on an $S^7$ bundle is applied to the dimensional reduction of eleven-dimensional supergravity and ten-dimensional superstring theory to four dimensions. A principle, consistent with higher-dimensional superstring theory, is suggested to explain the types of gauge interactions that arise in the standard model based on the geometry of the internal symmetry spaces. It is shown why a Lie group structure is required for vector bosons in pure gauge theories and that the application of division algebras to force unification must begin with the fermions comprising the elementary particle multiplets of the standard model. A suggestion is made for establishing a mechanism for the cancellation of anomalies within this approach to superstring theory.