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Analysis of zero modes for Dirac operators with magnetic links

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

n this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in (and ) 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 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.
OriginalsprogEngelsk
TidsskriftJournal of Functional Analysis
Vol/bind275
Udgave nummer3
Sider (fra-til)604-659
ISSN0022-1236
DOI
StatusUdgivet - 2018

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