Regular Connections among Generalized Connections

Details Regular Connections among Generalized Connections Regular Connections among Generalized Connections

2002-11-23

arxiv.org/abs/math-ph/0211060v1

J. Geom. Phys. 47 (2003) 469--483

Physics

Mathematical Physics

13 pages, 1 figure, LaTeX

Scientific paper

10.1016/S0393-0440(02)00232-2

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.

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