Chern-Simons theory, Stokes' theorem, and the Duflo map

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Sahlmann, Hanno¹  Thiemann, Thomas² 

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

[2] Univ Erlangen Nurnberg, Inst Theoret Phys 3, D-8520 Erlangen, Germany

关键词: Chern-Simons theory;    Duflo map;    Loop quantum gravity;   

DOI  :  10.1016/j.geomphys.2011.02.013

来源: Elsevier

【 摘 要 】

We consider a novel derivation of the expectation values of holonomies in Chern-Simons theory, based on Stokes' Theorem and the functional properties of the Chern-Simons action. It involves replacing the connection by certain functional derivatives under the path integral. It turns out that ordering choices have to be made in the process, and we demonstrate that, quite surprisingly, the Duflo isomorphism gives the right ordering, at least in the simple cases that we consider. In this way, we determine the expectation values of unknotted, but possibly linked, holonomy loops for SU(2) and SU(3), and sketch how the method may be applied to more complicated cases. Our manipulations of the path integral are formal but well motivated by a rigorous calculus of integration on spaces of generalized connections which has been developed in the context of loop quantum gravity. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free