Dirac算子指数与拓扑绝缘体的分类
Index of Dirac operators and classification of topological insulators
摘要：
研究实Clifford丛和复Clifford丛上的Dirac算子。利用Dirac算子的指数定理，从Clifford棋盘构造了拓扑不变量表.通过K理论群、Grothendieck群与对称空间的关系，得到了拓扑绝缘体和超导体的周期表。这就证明了实复拓扑相周期表是由Clifford棋盘和指数定理导出的。
英文摘要：
Real and complex Clifford bundles and Dirac operators defined on them are considered. By using the index theorems of Dirac operators, table of topological invariants is constructed from the Clifford chessboard. Through the relations between K-theory groups, Grothendieck groups and symmetric spaces, the periodic table of topological insulators and superconductors is obtained. This gives the result that the periodic table of real and complex topological phases is originated from the Clifford chessboard and index theorems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
