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On the support of the Ashtekar-Lewandowski measure

Donald Marolf·Jose M. Mourao
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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.

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Donald Marolf, Jose M. Mourao. 1994-03-18. On the support of the Ashtekar-Lewandowski measure. https://doi.org/10.1007/bf02099150

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