Abelian Chern-Simons theory, Stokes' theorem, and generalized connections

Sahlmann H, Thiemann T (2012)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2012


Publisher: Elsevier

Book Volume: 62

Pages Range: 204-212

Journal Issue: 2

DOI: 10.1016/j.geomphys.2011.10.012


Generalized connections and their calculus have been developed in the context of quantum gravity. Here we apply them to abelian Chern-Simons theory. We derive the expectation values of holonomies in U(1) Chern-Simons theory using Stokes' theorem, flux operators and generalized connections. A framing of the holonomy loops arises in our construction, and we show how, by choosing natural framings, the resulting expectation values nevertheless define a functional over gauge invariant cylindrical functions.The abelian theory considered in the present article is the test case for our method. It can also be applied to the non-abelian theory. Results will be reported in a companion article. © 2011 Elsevier B.V.

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Sahlmann, H., & Thiemann, T. (2012). Abelian Chern-Simons theory, Stokes' theorem, and generalized connections. Journal of Geometry and Physics, 62(2), 204-212. https://dx.doi.org/10.1016/j.geomphys.2011.10.012


Sahlmann, Hanno, and Thomas Thiemann. "Abelian Chern-Simons theory, Stokes' theorem, and generalized connections." Journal of Geometry and Physics 62.2 (2012): 204-212.

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