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arXiv · 1701.04987

Self-adjointness and spectral properties of Dirac operators with magnetic links

Fabian Portmann·Jérémy Sok·Jan Philip Solovej
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Abstract

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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Fabian Portmann, Jérémy Sok, Jan Philip Solovej. 2018-02-20. Self-adjointness and spectral properties of Dirac operators with magnetic links. https://arxiv.org/abs/1701.04987

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