Dirac operators on quasi-Hamiltonian G-spaces

Yanli Song

doi:10.1016/j.geomphys.2016.01.012

Dirac operators on quasi-Hamiltonian G-spaces

Yanli Song

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	70-86
Number of pages	17
Journal	Journal of Geometry and Physics
Volume	106
DOIs	https://doi.org/10.1016/j.geomphys.2016.01.012
State	Published - Aug 1 2016

Keywords

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

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10.1016/j.geomphys.2016.01.012

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title = "Dirac operators on quasi-Hamiltonian G-spaces",

abstract = "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.",

keywords = "Dirac operators, Geometric quantization, Loop group, Quasi-Hamiltonian G-space",

author = "Yanli Song",

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T1 - Dirac operators on quasi-Hamiltonian G-spaces

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AB - 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.

KW - Dirac operators

KW - Geometric quantization

KW - Loop group

KW - Quasi-Hamiltonian G-space

UR - https://www.scopus.com/pages/publications/84961711433

U2 - 10.1016/j.geomphys.2016.01.012

DO - 10.1016/j.geomphys.2016.01.012

M3 - Article

AN - SCOPUS:84961711433

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VL - 106

SP - 70

EP - 86

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

ER -

Dirac operators on quasi-Hamiltonian G-spaces

Abstract

Keywords

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