Degeneracy of zero modes of the Dirac operator in three dimensions

Details Degeneracy of zero modes of the Dirac operator in three dimensions Degeneracy of zero modes of the Dirac operator in three dimensions

1999-10-18

arxiv.org/abs/hep-th/9910139v1

Phys.Lett. B485 (2000) 314-318

Physics

High Energy Physics

High Energy Physics - Theory

Latex file, 7 pages

Scientific paper

10.1016/S0370-2693(00)00701-2

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.

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