Regular connections among generalized connections

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...

Properties of Generalized Berwald Connections

properties of generalized berwald connections

Construction of Generalized Connections

We present a construction method for mappings between generalized connections, comprising, e.g., the action of gauge transformations, diffeomorphisms and Weyl transformations. Moreover, criteria for continuity and measure preservation are stated.

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...