Connections in the manifold admitting generalized transformations

Connections and Generalized Gauged Transformations

With the standard fibre being a coset manifold, the transformation of a connection form in a fibre bundle under the action of the isometry group includes a dependence on the fibre coordinate. Elimination of the fibre coordinate from the transformation rule implies that the standard fibre is a Lie group and that the bundle is a principal bundle. The dependence on the fibre coordinate is consider...

Properties of Generalized Berwald Connections

Transformations of Sheaf Connections

After a brief survey of the primary ideas involved in the theory of connections on vector and principal sheaves (studied in [7], [8], [14], [15]), we examine the behaviour of connections under various types of morphisms between sheaves of the considered category. The results thus obtained are useful in the development of a non-smooth geometry in the aforementioned abstract framework and related...

Regular Connections among Generalized Connections

The properties of the space A of regular connections as a subset of the space A of generalized connections in the Ashtekar framework are studied. For every choice of compact structure group and smoothness category for the paths it is determined whether A is dense in A or not. Moreover, it is proven that A has Ashtekar-Lewandowski measure zero for every nontrivial structure group and every smoot...

Diffeomorphism-invariant Generalized Measures On the Space of Connections Modulo Gauge Transformations

The notion of a measure on the space of connections modulo gauge transformations that is invariant under diffeomorphisms of the base manifold is important in a variety of contexts in mathematical physics and topology. At the formal level, an example of such a measure is given by the Chern-Simons path integral. Certain measures of this sort also play the role of states in quantum gravity in Asht...