定向折叠上Dirac算子的构造
The Construction of Dirac Operators on Orientifolds
摘要：
受维格纳定理的启发，描述了一个规范的构造，它产生了一个既具有酉对称性又具有反酉对称性的Atiyah-Singer Dirac算子。这个狄拉克算子包括作为特殊情况的KR理论的狄拉克算子，填补了文献中长期存在的空白。为了构造这种结构，利用半等变的Dixmier-Douady理论定义并分类了定向折叠的Spin-c-结构，并证明了关于Spin-c-结构存在性的几个标准定理的类似定理.
英文摘要：
Motivated by Wigner's theorem, a canonical construction is described that produces an Atiyah-Singer Dirac operator with both unitary and anti-unitary symmetries. This Dirac operator includes the Dirac operator for KR-theory as a special case, filling a long-standing gap in the literature. In order to make the construction, orientifold Spin-c-structures are defined and classified using semi-equivariant Dixmier-Douady theory, and analogues of several standard theorems on the existence of Spin-c-structures are proved.
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