2017/05/08 by Portmann, Fabian, Sok, Jeremy, Solovej, Jan Philip
#58C40 #81Q10 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1705.02959
In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in \mathbbS3 (and ℝ3) by Dirac operators with smooth magnetic fields. We then proceed to prove that under certain assumptions, the spectral flow of paths along these operators is the same in both the smooth and the singular case. We recently characterized the spectral flow of such paths in the singular case. This allows us to show the existence of new smooth, compactly supported magnetic fields in ℝ3 for which the associated Dirac operator has a non-trivial kernel. Using Clifford analysis, we also obtain criteria on the magnetic link for the non-existence of zero modes.