On the non-existence of zero modes

Daniel M. Elton
2018 Opuscula Mathematica  
We consider magnetic fields on R 3 which are parallel to a conformal Killing field. When the latter generates a simple rotation we show that a Weyl-Dirac operator with such a magnetic field cannot have a zero mode. In particular this allows us to expand the class of non zero mode producing magnetic fields to include examples of non-trivial smooth compactly supported fields.
doi:10.7494/opmath.2018.38.4.537 fatcat:mx4cbtq735dg7ixta36bau5lsa