无质量Dirac费米子的Aharonov-Bohm效应和经典边界条件下Dirac型算子的谱流
The Aharonov-Bohm effect for massless Dirac fermions and the spectral flow of Dirac type operators with classical boundary conditions
摘要：
本文在紧致有界黎曼流形上，用拓扑方法计算了任意一族具有经典（局部）边界条件的自伴Dirac型算子的谱流，并假设该算子族的初算子和终算子是由丛自同构共轭的.利用这一结果研究了具有非平凡拓扑的二维区域中一族具有局部边界条件的自伴Dirac型算子的非零谱流存在的条件.讨论了非零谱流的可能物理实现。
英文摘要：
We compute, in topological terms, the spectral flow of an arbitrary family of self-adjoint Dirac type operators with classical (local) boundary conditions on a compact Riemannian manifold with boundary under the assumption that the initial and terminal operators of the family are conjugate by a bundle automorphism. This result is used to study conditions for the existence of nonzero spectral flow of a family of self-adjoint Dirac type operators with local boundary conditions in a two-dimensional domain with nontrivial topology. Possible physical realizations of nonzero spectral flow are discussed.
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