Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1894541 | Journal of Geometry and Physics | 2016 | 17 Pages |
Abstract
We construct twisted spinor bundles as well as twisted pre-quantum bundles on quasi-Hamiltonian GG-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 GG-spaces to quasi-Hamiltonian GG-spaces.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Yanli Song,