Kaluza–Klein or fibre bundles?

Two basic geometric ways in the modern theory of the gauge fields are analyzed and compared. The first way is an extension of the Kaluza–Klein unified theory of gravity and electromagnetism (1921). The second way extends the Cartan's formulation (1925) of Riemannian geometry and GR which is transformed to the fibre bundle theory now. The goal of this talk is to show that above-mentioned two geometric ways in the classical gauge fields theory are nonequivalent and lead to different forms of the quantum gauge fields theory. Bibliography: 12 titles.