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A Mathematical Construction of the Non-Abelian Chern-Simons Functional Integral

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Abstract:

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.

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  1. Fakultät und Institut für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany, , , , , , DE

    Sergio Albeverio & Ambar Sengupta

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  1. Sergio Albeverio
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  2. Ambar Sengupta
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Received: 2 April 1996 / Accepted: 15 August 1996

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Albeverio, S., Sengupta, A. A Mathematical Construction of the Non-Abelian Chern-Simons Functional Integral . Comm Math Phys 186, 563–579 (1997). https://doi.org/10.1007/s002200050120

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  • DOI: https://doi.org/10.1007/s002200050120

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