Opuscula Math. 38, no. 4 (2018), 537-556
https://doi.org/10.7494/OpMath.2018.38.4.537

Opuscula Mathematica

# On the non-existence of zero modes

Daniel M. Elton

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.

Keywords: Weyl-Dirac operator, zero modes.

Mathematics Subject Classification: 35J46, 35P20, 35Q40, 81Q10.

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• Daniel M. Elton
• Lancaster University, Fylde College, Department of Mathematics and Statistics, Lancaster LA1 4YF, United Kingdom
• Communicated by Sergey N. Naboko.
• Accepted: 2017-12-11.
• Published online: 2018-04-11.