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

2017/01/18 by Portmann, Fabian, Sok, Jérémy, Solovej, Jan Philip
#57M25 (Secondary) #58C40 #81Q10 (Primary) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1701.04987

Abstract

We define Dirac operators on \mathbbS³ (and ℝ³) 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 \mathbbS³, are investigated in detail and we compute the dimension of the zero-energy eigenspace.

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