标题： 基灵-杨张量，非标准超对称性和一个指标定理 显示英文标题

标题： Killing-Yano tensors, non-standard supersymmetries and an index theorem

摘要： 通过自旋粒子可以探测时空中Killing-Yano张量的存在。 具体而言，狄拉克粒子具有对应于粒子世界线上的非标准超对称性的新的费米子守恒量。 几何对偶性将具有Killing-Yano结构但无扭率的时空与其他具有Killing-Yano结构和扭率的时空联系起来。 双时空上狄拉克算子指标之间的关系允许将具有扭率的时空的指标表示为无扭率的时空的指标。 显示英文摘要

摘要： The existence of Killing-Yano tensors on space-times can be probed by spinning particles. Specifically, Dirac particles possess new fermionic constants of motion corresponding to non-standard supersymmetries on the particle worldline. A geometrical duality connects space-times with Killing-Yano structure, but without torsion, to other space-times with Killing-Yano structure and torsion. A relation between the indices of the Dirac operators on the dual space-times allows to express the index on the space-time with torsion in terms of that of the space-time without torsion.