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The Wilson Loop Observables of Chern-Simons Theory on ℝ3 in Axial Gauge

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Abstract

We define the Wilson loop observables (WLOs) for pure Chern-Simons models with base manifold M=ℝ3 rigorously as infinite dimensional oscillatory integrals by exploiting an ‘‘axial gauge fixing’’ and applying certain regularization techniques like ‘‘loop-smearing’’ and ‘‘framing’’. The values of the WLOs can be computed explicitly. If the structure group G of the model considered is Abelian one obtains well-known linking number expressions for the WLOs. If G is Non-Abelian one obtains expressions which are similar but not identical to the state sum representations for the Homfly and Kauffman polynomials by Jones and Turaev.

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  1. Institut für Angewandte Mathematik der Universität Bonn, Wegelerstraße 6, 53115, Bonn, Germany

    Atle Hahn

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  1. Atle Hahn
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Communicated by M.R. Douglas

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Hahn, A. The Wilson Loop Observables of Chern-Simons Theory on ℝ3 in Axial Gauge. Commun. Math. Phys. 248, 467–499 (2004). https://doi.org/10.1007/s00220-004-1097-4

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