Nonminimal field theory: I. Extension of the Einstein-Yang-mills model

Nonminimal field theory stands to extend the idea of geometrization of the interaction models of physical systems with the gravity field by introducing new cross-couplings, in which the space-time curvature plays a key role. At present time this science is considered only as a formal unification of the models of nonminimal coupling between scalar, pseudoscalar, vector, gauge fields and gravity. Now we faced with the problem of formulation of basic principles of the nonminimal field theory as a new science. In this work we discuss some general aspects of the nonminimal field theory construction by the example of gauge interactions, and illustrate some principally new results, which we have obtained in the framework of the nonminimal Einstein-Yang-Mills model.