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

JOURNAL OF GEOMETRY AND PHYSICS

卷:62

Article

Sahlmann, Hanno^1,2  Thiemann, Thomas^3,4,5 

[1] POSTECH, Asia Pacific Ctr Theoret Phys, Pohang 790784, South Korea

[2] Pohang Univ Sci & Technol, Dept Phys, Pohang, South Korea

[3] Erlangen Univ, Inst Theoret Phys 3, Erlangen, Germany

[4] Max Planck Inst Gravitat Phys, Potsdam, Germany

[5] Perimeter Inst Theoret Phys, Waterloo, ON, Canada

关键词: Abelian Chern-Simons theory;    Loop quantum gravity;    Generalized connections;   

DOI  :  10.1016/j.geomphys.2011.10.012

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free