Abstract

In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in S3 (and R3) by Dirac operators with smooth magnetic fields. Then we 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.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.