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

Understand

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.