Opuscula Math. 38, no. 4 (2018), 537-556

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.
  • Received: 2017-11-30.
  • Accepted: 2017-12-11.
  • Published online: 2018-04-11.
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Cite this article as:
Daniel M. Elton, On the non-existence of zero modes, Opuscula Math. 38, no. 4 (2018), 537-556, https://doi.org/10.7494/OpMath.2018.38.4.537

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