On the support of the Ashtekar-Lewandowski measure

Details On the support of the Ashtekar-Lewandowski measure On the support of the Ashtekar-Lewandowski measure

1994-03-18

arxiv.org/abs/hep-th/9403112v1

Commun.Math.Phys. 170 (1995) 583-606

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1007/BF02099150

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.

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