Regular Connections among Generalized Connections

Abstract

The properties of the space $\A$ of regular connections as a subset of the space $\Ab$ 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 $\Ab$ or not. Moreover, it is proven that $\A$ has Ashtekar-Lewandowski measure zero for every nontrivial structure group and every smoothness category. The analogous results hold for gauge orbits instead of connections.

13 pages, 1 figure, LaTeX

References in corpus (5)

• Diffeomorphism invariant Quantum Field Theories of Connections in terms of webs
• Hyphs and the Ashtekar-Lewandowski Measure
• Stratification of the Generalized Gauge Orbit Space
• On the Spectrum of Holonomy Algebras
• On the Spectrum of Holonomy Algebras

Cited by in corpus (2)

• Representations of the Weyl Algebra in Quantum Geometry
• Thin homotopy and the holonomy approach to gauge theories