On the non-existence of zero modes

Abstract

We consider magnetic fields on ${\mathbb{R}}^3$ 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.

arXiv comment21 pages