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

## TL;DR

This paper investigates Dirac operators with magnetic fields supported on links in three-dimensional spaces, establishing their self-adjointness and spectral characteristics, including discrete spectra and zero-energy states.

## Contribution

It introduces a framework for defining and analyzing Dirac operators with magnetic links, proving self-adjointness and exploring spectral properties in detail.

## Key findings

- Operators have discrete spectra
- Zero-energy eigenspaces are characterized
- Explicit examples like circles are analyzed

## 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.