A Mathematical Construction of the Non-Abelian Chern-Simons Functional Integral
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We construct rigorously an infinite dimensional distribution which corresponds to the Chern-Simons (CS) functional integral associated with a principal fiber bundle over R 3 with structure group a compact connected Lie group. We determine the ‘moments’ of the CS distribution and show that these coincide with those used in informal studies of the CS integral. A locality property of the CS distribution is proven. The complexified theory of Fröhlich and King is also discussed within our framework.
KeywordsStructure Group Fiber Bundle Locality Property Complexify Theory Functional Integral
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