A sharp criterion for zero modes of the Dirac equation
Rupert L. Frank
Ludwig-Maximilians Universität München, München, Germany; Munich Center for Quantum Science and Technology, München, Germany; California Institute of Technology, Pasadena, USAMichael Loss
Georgia Institute of Technology, Atlanta, USA
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Abstract
It is shown that is a necessary condition for the existence of a nontrivial solution of the Dirac equation in dimensions. Here, is the sharp Sobolev constant. If is odd and , then there exist vector potentials that allow for zero modes. A complete classification of these vector potentials and their corresponding zero modes is given.
Cite this article
Rupert L. Frank, Michael Loss, A sharp criterion for zero modes of the Dirac equation. J. Eur. Math. Soc. (2024), published online first
DOI 10.4171/JEMS/1475