### Abstract

It is investigated that the structure of the kernel of the Dirac-Weyl operator D of a charged particle in the magnetic-field B = B_{0} + B_{1}, given by the sum of a strongly singular magnetic field B_{0} (·) = Σ_{v}γ^{v} δ(· - a_{v} with some singular points a_{v} and a magnetic-field B_{1} with a bounded support. Here the magnetic field B_{1} may have some singular points with the order of the singularity less than 2. At a glance, it seems that, following "Aharonov-Casher Theorem" [Phys. Rev. A 19, 2461 (1979)], the dimension of the kernel of D, dimker D, is a function of one variable of the total magnetic flux ( = Σ_{v}γ_{v} + ∫_{R}2B_{1}dxdy) of B. However, since the influence of the strongly singular points works, dim ker D indeed is a function of several variables of the total magnetic flux and each of y_{v}'s.

Original language | English |
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Pages (from-to) | 3334-3343 |

Number of pages | 10 |

Journal | Journal of Mathematical Physics |

Volume | 42 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 1 2001 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Mathematical Physics*,

*42*(8), 3334-3343. https://doi.org/10.1063/1.1379312