Symplectic Killing spinors

Commentationes mathematicae Universitatis Carolinae

Svatopluk Krýsl¹ 

关键词: Fedosov manifolds;    symplectic spinors;    symplectic Killing spinors;    symplectic Dirac operators;    Segal-Shale-Weil representation;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

Let $(M,\omega )$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla$. Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one may easily compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere $S^2$ equipped with the volume form of the round metric.

【 授权许可】

CC BY