On the support of the Ashtekar-Lewandowski measure

Abstract

We show that the Ashtekar-Isham extension of the classical configuration space of Yang-Mills theories (i.e. the moduli space of connections) is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices. These results are then used to prove that the classical configuration space is contained in a zero measure subset of this extension with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure. Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the ``extended" configuration space.

22 pages, Tex, Preprint CGPG-94/3-1

References in corpus (2)

• Representations of the holonomy algebras of gravity and non-Abelian gauge theories
• Representation Theory of Analytic Holonomy C* Algebras

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