Abstract
We show that the Ashtekar-Isham extension\(\overline {A/G}\) of the configuration space of Yang-Mills theories\(A/G\) 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\(A/G\) is contained in a zero measure subset of\(\overline {A/G}\) with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on\(\overline {A/G}\). 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\(\overline {A/G}\).
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Communicated by S.-T. Yau
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Marolf, D., Mourão, J.M. On the support of the Ashtekar-Lewandowski measure. Commun.Math. Phys. 170, 583–605 (1995). https://doi.org/10.1007/BF02099150
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DOI: https://doi.org/10.1007/BF02099150