Connections on distributional bundles (Q2504917)

The author studied in his previous paper [Arch. Math., Brno 36, No. 2, 111--124 (2000; Zbl 1050.46515)] smooth bundles whose fibers are distribution spaces. In this paper his investigations are extended to the general case of the bundle of generalized tube sections of a 2-fibered finite dimensional bundle. Tangent space, jet space, connection and curvature are introduced. Existence of adjoint- and tensor product-connections are shown. It is proved that a suitable connection on the underlying classical bundle yields a connection on the corresponding distributional bundle. A few examples relevant to quantum fields theory are discussed. Throughout the paper also coordinate expressions are given.