具有奇异磁场的Pauli算子零模的无限性
Infiniteness of zero modes for the Pauli operator with singular magnetic field
摘要：
我们建立了描述自旋为1/2的二维量子系统的Pauli算符在一定条件下具有无限维的零模空间，可能是自旋向上和自旋向下的零模，而且零本征值与谱的其余部分之间存在谱隙.特别地，如果场具有无穷大通量，则无穷大发生，这解决了Aharonov-Casher定理的这个先前未知的情况。
英文摘要：
We establish that the Pauli operator describing a spin-1/2 two-dimensional quantum system with a singular magnetic field has, under certain conditions, an infinite-dimensional space of zero modes, possibly, both spin-up and spin-down, moreover there is a spectral gap separating the zero eigenvalue from the rest of the spectrum. In particular, infiniteness takes place if the field has infinite flux, which settles this previously unknown case of Aharonov-Casher theorem.
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