Self-adjointness and spectral properties of Dirac operators with magnetic links
We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum. C...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with
magnetic fields supported on smooth, oriented links and prove self-adjointness
of certain (natural) extensions. We then analyze their spectral properties and
show, among other things, that these operators have discrete spectrum. Certain
examples, such as circles in $\mathbb{S}^3$, are investigated in detail and we
compute the dimension of the zero-energy eigenspace. |
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| DOI: | 10.48550/arxiv.1701.04987 |