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

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. (C) 2011 Elsevier B.V. All rights reserved.