Dirac operators on quasi-Hamiltonian G-spaces

JOURNAL OF GEOMETRY AND PHYSICS

卷:106

Article

Song, Yanli¹ 

[1] Univ Toronto, Toronto, ON M5S 1A1, Canada

关键词: Dirac operators;    Geometric quantization;    Quasi-Hamiltonian G-space;    Loop group;   

DOI  :  10.1016/j.geomphys.2016.01.012

来源: Elsevier

【 摘 要 】

We construct twisted spinor bundles as well as twisted pre-quantum bundles on quasi Hamiltonian G-spaces, using the spin representation of loop group and the Hilbert space of Wess-Zumino-Witten model. We then define a Hilbert space together with a Dirac operator acting on it. The main result of this paper is that we show the Dirac operator has a well-defined index given by positive energy representation of the loop group. This generalizes the geometric quantization of Hamiltonian G-spaces to quasi-Hamiltonian G-spaces. Crown Copyright (C) 2016 Published by Elsevier B.V. All rights reserved.

【 授权许可】

Free