论文标题
半法和Callias操作员的光谱本地化
Spectral localization for semimetals and Callias operators
论文作者
论文摘要
半经典论证用于表明自我跳动操作员（所谓的光谱定位器）的低覆盖光谱决定了理想半学的狄拉克或Weyl点的数量。除了IMS本地化程序外，Dirac或Weyl Point给出的本地玩具模型的明确计算是证明的关键要素。该论点与维滕的推理有许多相似之处，导致莫尔斯的不平等现象。相同的技术允许在自助式弗雷德霍尔姆操作员的多参数光谱方面证明Callias运算符的光谱定位。
A semiclassical argument is used to show that the low-lying spectrum of a selfadjoint operator, the so-called spectral localizer, determines the number of Dirac or Weyl points of an ideal semimetal. Apart from the IMS localization procedure, an explicit computation for the local toy models given by a Dirac or Weyl point is the key element of proof. The argument has numerous similarities to Witten's reasoning leading to the strong Morse inequalities. The same techniques allow to prove a spectral localization for the Callias operator in terms of a multi-parameter spectral flow of selfadjoint Fredholm operators.
