Jordan-Kaluza-Klein type unified theories of gauge and gravity fields.

Abstract

Having adopted this picture, however, it is necessary to insure that the resulting theory be internally consistent. Specifically, it is required that covariant derivatives calculated from the connection on the total bundle space agree with those calculated from the gravity connection on spacetime and the gauge connection on the bundle. I will show that this requirement eliminates the components of the total bundle space metric corresponding to the group dimensions as degrees of freedom in the theory. For arbitrary gauge fields, this part of the metric is in fact required to be invariant under the action of the group and its components must be spacetime constants. This sheds new light on the traditional construction of gauge theories, since this type of metric has long been the standard one adopted in their developement. Potentially troublesome scalar-tensor versions of this theory are also ruled out by this requirement.

Given such a structure, it is tempting to regard the total bundle space as the true arena for particle interactions. I will show that this can in fact be done, since spacetime tensor fields and fields in the Lie algebra of the structure group of the bundle may also be regarded as fields within the tangent space of the bundle.

In this thesis I study generalizations of Jordan-Kaluza-Klein unified field theories which are based on a principle fiber bundle erected over spacetime. These theories follow the standard general relativistic procedure in that gravitation is described by a (metric compatible) affine connection on spacetime. Gauge fields are assumed to arise from the more general notion of a connection on the bundle. The two types of fields are combined by means of the affine connection on the total bundle space.