Finsler and Kaluza-Klein gauge theories (Q1309002)

The author develops a gauge theory on the total space \(E\) of a vector bundle with respect to the transformations (1) \(\bar x^ i = \bar x^ i(x^ 1,\dots,x^ m)\); \(\bar z^ a = L^ a_ b(x)z^ b\), \(i\in\{1,\dots,m\}\), \(a,b \in \{1,\dots,n\}\). It is shown that Kaluza- Klein theory and a Finsler gauge approach exist simultaneously and define two different representations of the transformation group. The components of the nonlinear connection on \(E\) are considered as potentials and fields with respect to a Kaluza-Klein theory and a Finsler gauge theory respectively. The transformations (1) contain the Asanov's gauge transformations [cf. \textit{G. A. Asanov}, Finsler geometry, relativity and gauge theories (1985; Zbl 0576.53001)]. The general gauge transformations on a total space of a fibre bundle are considered by the reviewer [Finsler geometry and applications (1990; Zbl 0702.53001)] in a chapter on gauge theory on a fibre bundle.