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| Format: | Preprint |
| Published: |
2023
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| Online Access: | https://arxiv.org/abs/2304.13373 |
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| _version_ | 1866908600803262464 |
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| author | Fialová, Marie |
| author_facet | Fialová, Marie |
| contents | The Aharonov-Casher theorem is a result on the number of the so-called zero modes of a system described by the magnetic Pauli operator in $\mathbb{R}^2$. In this paper we address the same question for the Dirac operator on a flat two-dimensional manifold with boundary and Atiyah-Patodi-Singer boundary condition. More concretely we are interested in the plane and a disc with a finite number of circular holes cut out. We consider a smooth compactly supported magnetic field on the manifold and an arbitrary magnetic field inside the holes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13373 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Aharonov-Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition Fialová, Marie Mathematical Physics Spectral Theory The Aharonov-Casher theorem is a result on the number of the so-called zero modes of a system described by the magnetic Pauli operator in $\mathbb{R}^2$. In this paper we address the same question for the Dirac operator on a flat two-dimensional manifold with boundary and Atiyah-Patodi-Singer boundary condition. More concretely we are interested in the plane and a disc with a finite number of circular holes cut out. We consider a smooth compactly supported magnetic field on the manifold and an arbitrary magnetic field inside the holes. |
| title | Aharonov-Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition |
| topic | Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2304.13373 |