Fields in nonaffine bundles. I. The general bitensorially gauge-covariant differentiation procedure

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Abstract
The standard covariant differentiation procedure for fields in vector bundles is generalized so as to be applicable to fields in general nonaffine bundles in which the fibers may have an arbitrary nonlinear structure. In addition to the usual requirement that the base space should be flat or endowed with its own linear connection Γ, and that there should be an ordinary gauge connection A on the bundle, it is necessary to require also that there should be an intrinsic, bundle-group-invariant connection Γ^ on the fiber space. The procedure is based on the use of an appropriate primary-field- (i.e., section-) dependent connector ω that is constructed in terms of the natural fiber-tangent-vector realization A of the gauge connection. The application to gauged-harmonic mappings will be described in the following article.
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