Extensions of the Duflo map and Chern-Simons expectation values

JOURNAL OF GEOMETRY AND PHYSICS

卷:121

Article

Sahlmann, Hanno¹  Zilker, Thomas¹ 

[1] Friedrich Alexander Univ Erlangen Nurnberg, Inst Quantum Grav, Staudtstr 7-B2, D-91058 Erlangen, Germany

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

DOI  :  10.1016/j.geomphys.2017.07.022

来源: Elsevier

【 摘 要 】

The Duflo map is a valuable tool for operator ordering in contexts in which the Kirillov-Kostant-Souriau bracket and its quantization play a role. It has beautiful properties on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. In the present work, we focus on its action beyond this subspace: We calculate the image of the exponential map, to obtain a certain deformation of SU(2), and we discuss and compare modifications of its action on non-invariant elements. Also, an application to the calculation of Chern-Simons theory expectation values is discussed. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free