Abelian Chern-Simons theory, Stokes%26apos; theorem, and generalized connections

作者：Sahlmann Hanno^*; Thiemann Thomas

来源：Journal of Geometry and Physics, 2012, 62(2): 204-212.

DOI：10.1016/j.geomphys.2011.10.012

• Abelian Chern-Simons theory
• Loop quantum gravity
• 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%26apos; 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. %26lt;br%26gt;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.

• 出版日期2012-2