Abstract
Publisher Summary The gauge principle is the basis for generating unified field theories for elementary particle interactions. It is used to arrive at a formulation of general relativity (G.R.) in terms of elementary matter and gauge fields. The formal structure of all such theories is described in the language of fiber bundles. Such an approach serves both to clarify the essential differences between the intrinsic and the space-time-based gauge field theories and also to provide a framework for extending the underlying geometrical structure of G.R. The approach of elementary particle theorists starts with a Lagrangian, generating a set of field equations that are invariant under a group of internal-symmetry transformations of the rigid variety. Then, through a minimal replacement of the ordinary derivatives by the covariant ones, the new equations are made invariant under the nonrigid actions of the group. When the same approach is applied to a nonintrinsic symmetry group, which acts upon the space-time points themselves, the notion of nonrigid actions becomes more subtle, and one is obliged to introduce independent reference frames attached to the various space-time points.
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