Dirac operators on quasi-Hamiltonian G-spaces

作者：Song Yanli^*

来源：Journal of Geometry and Physics, 2016, 106: 70-86.

DOI：10.1016/j.geomphys.2016.01.012

• Dirac operators
• Geometric quantization
• Quasi-Hamiltonian G-space
• Loop group

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.

• 出版日期2016-8