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

Beitrag in einer Fachzeitschrift
(Originalarbeit)


Details zur Publikation

Autorinnen und Autoren: Sahlmann H, Thiemann T
Zeitschrift: Journal of Geometry and Physics
Verlag: Elsevier
Jahr der Veröffentlichung: 2011
Band: 61
Heftnummer: 6
Seitenbereich: 1104-1121
ISSN: 0393-0440


Abstract


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. © 2011 Elsevier B.V.



FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Sahlmann, Hanno Prof. Dr.
Professur für Theoretische Physik
Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik


Zitierweisen

APA:
Sahlmann, H., & Thiemann, T. (2011). Chern-Simons theory, Stokes' theorem, and the Duflo map. Journal of Geometry and Physics, 61(6), 1104-1121. https://dx.doi.org/10.1016/j.geomphys.2011.02.013

MLA:
Sahlmann, Hanno, and Thomas Thiemann. "Chern-Simons theory, Stokes' theorem, and the Duflo map." Journal of Geometry and Physics 61.6 (2011): 1104-1121.

BibTeX: 

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