An Analytic Approach to Turaev’s Shadow Invariant
نویسنده
چکیده
Abstract. In the present paper we extend the “torus gauge fixing approach” by Blau & Thompson, which was developed in [8] for the study of ChernSimons models with base manifolds M of the form M = Σ× S1, in a suitable way. We arrive at a heuristic path integral formula for the Wilson loop observables associated to general links in M . The heuristic measures that appear in this formula are all of “Gaussian type”, and it is thus possible to find a rigorous realization of the path integral expressions by applying results from white noise analysis and by making use of regularization techniques like “loop smearing” and “framing”. Finally, we demonstrate that the explicit evaluation of the aforementioned path integral expressions naturally leads to the face models of statistical mechanics in terms of which Turaev’s shadow invariant is defined.
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