Multiple 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 construction of multiple zero modes has been sucessfully carried out only very recently. Here we generalise these results by discussing a much wider class of Dirac operators together with their zero modes. Further we show that those Dirac operators that do admit zero modes may be related to Hopf maps, where the Hopf index is related to the number of zero modes in a simple way.

Latex file, 20 pages, no figures

References in corpus (4)

• Creation and evolution of magnetic helicity
• Degeneracy of zero modes of the Dirac operator in three dimensions
• Hopf instantons in Chern-Simons theory
• Hopf instantons and the Liouville equation in target space

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• Recent developments in quantum mechanics with magnetic fields
• Abelian Zero Modes in Odd Dimensions
• The asymptotic limits of zero modes of massless Dirac operators
• Chern-Simons action for zero-mode supporting gauge fields in three dimensions
• The zero modes and zero resonances of massless Dirac operators
• On Absence of Threshold Resonances for Schrodinger and Dirac Operators
• Fermion Zero Modes in Odd Dimensions
• Stability of QED
• Non-Abelian Thermal Large Gauge Transformations in 2+1 Dimensions
• The symmetries of the Dirac--Pauli equation in two and three dimensions
• Eigenfunctions of Dirac operators at the threshold energies