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

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

2010-04-16

arxiv.org/abs/1004.2834v3

Journal of Geometry and Physics 62 (2) (2012) 204-212

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 4 figures; v3: material about natural framings collected in one section, typos removed. This version identical to pu

Scientific paper

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 test case for our method. It can also be applied to the non-abelian theory. Results for that case will be reported elsewhere.

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