Abstract
Two basic geometric approaches to the modern theory of gauge fields are analyzed and compared. The first approach is an extension of the Kaluza-Klein unified theory of gravity and electromagnetism (1921). The second approach generalizes Cartan's formulation (1925) of Riemannian geometry and GR which now is transformed to fiber bundle theory. The goal of this paper is to show that the above-mentioned geometric approaches to the classical gauge field theory are nonequivalent and lead to different forms of quantum gauge field theory. Bibliography:12 titles.
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