On the non-existence of zero modes

Elton, Daniel Mark (2018) On the non-existence of zero modes. Opuscula Mathematica, 38 (4). pp. 537-566. ISSN 1232-9274

Preview

PDF (noZM_OM)
noZM_OM.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial-NoDerivs.
Download (320kB)

Abstract

We consider magnetic fields on R3 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.