On the Ashtekar-Lewandowski measure as a restriction of the product one
- 1 December 2014
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 55 (12)
- https://doi.org/10.1063/1.4902931
Abstract
It is known that the $k$-dimensional Hausdorff measure on a $k$-dimensional submanifold of $\mathbb{R}^n$ is closely related to the Lebesgue measure on $\mathbb{R}^n$. We show that the Ashtekar-Lewandowski measure on the space of generalized $G$-connections for a compact, semi-simple, Lie group $G$, is analogously related to the product measure on the set of all $G$-valued functions on the group of loops. We also show that, the Ashtekar-Lewandowski measure is, under very mild conditions, supported on nowhere-continuous generalized connections.Comment: 11 pages, RevTeX, several explanations clarified and expanded with no change to the results, 3 references added, typos fixe
This publication has 6 references indexed in Scilit:
- Automatic Continuity of Group HomomorphismsBulletin of Symbolic Logic, 2009
- Parallel transports in websMathematische Nachrichten, 2003
- Physical properties of quantum field theory measuresJournal of Mathematical Physics, 1999
- Diffeomorphism-invariant quantum field theories of connections in terms of websClassical and Quantum Gravity, 1999
- Functional Integration on Spaces of ConnectionsJournal of Functional Analysis, 1997
- Topological quantum field theoryCommunications in Mathematical Physics, 1988