English

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

Mathematical Physics 2018-02-21 v3 math.MP

Abstract

We define Dirac operators on S3\mathbb{S}^3 (and R3\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 S3\mathbb{S}^3, are investigated in detail and we compute the dimension of the zero-energy eigenspace.

Keywords

Cite

@article{arxiv.1701.04987,
  title  = {Self-adjointness and spectral properties of Dirac operators with magnetic links},
  author = {Fabian Portmann and Jérémy Sok and Jan Philip Solovej},
  journal= {arXiv preprint arXiv:1701.04987},
  year   = {2018}
}