Degeneracy of zero modes of the Dirac operator in three dimensions

Abstract

One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the question whether such multiple zero modes may exist has remained unanswered until now. Here we prove that the feature of zero mode degeneracy indeed occurs for the Abelian Dirac operator in three dimensions, by explicitly constructing a class of Dirac operators together with their multiple zero modes. Further, we discuss some implications of our results, especially a possible relation to the topological feature of Hopf maps.

Latex file, 7 pages

References in corpus (2)

• Hopf instantons in Chern-Simons theory
• Hopf instantons and the Liouville equation in target space

Cited by in corpus (15)

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• Hopf maps as static solutions of the complex eikonal equation
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• Eigenfunctions at the threshold energies of magnetic Dirac operators
• Zero modes in finite range magnetic fields
• Abelian Zero Modes in Odd Dimensions
• A criterion for the existence of zero modes for the Pauli operator with fastly decaying fields
• The asymptotic limits of zero modes of massless Dirac operators
• Chern-Simons action for zero-mode supporting gauge fields in three dimensions
• Fermion Zero Modes in Odd Dimensions
• Stability of QED
• The symmetries of the Dirac--Pauli equation in two and three dimensions
• Asymptotics for Erdos-Solovej Zero Modes in Strong Fields