Chern-Simons models on \(S^2\times S^1\), torus gauge fixing, and link invariants. I
The paper is devoted to studies of Abelian and non-Abelian Chern-Simons models on manifolds \(M\) of the form \(M=\Sigma\times S^1\), where \(\Sigma\) is a compact oriented surface. By applying the ``torus gauge fixing'' procedure of \textit{M. Blau} and \textit{G. Thompson} [Nucl. Phys. B 408, 345--390 (1993; Zbl 1043.58502), Lectures on 2D gauge theories: topological aspects and path integral techniques, E. Gava, et al. (eds.), Proceedings of the 1993 Trieste Summer School on High Energy Physics and Cosmology, World Scientific, Singapore, 175--244 (1994)] the author derives a heuristic integral formula for the corresponding Wilson loop observables. It is shown that in the case of \(\Sigma = S^2\) and structure group \(U(1)\) this formula gives a rigorous path integral representation for the Wilson loop observables in terms of infinite-dimensional oscillatory integrals.
scientific article; zbMATH DE number 2175219
scientific article