Zero modes of the Dirac operator in three dimensions

Abstract

We investigate zero modes of the Dirac operator coupled to an Abelian gauge field in three dimensions. We find that the existence of a certain class of zero modes is related to a specific topological property precisely when the requirement of finite Chern--Simons action is imposed.

13 pages, 6 figures, uses the macro psbox.tex, replaced by a revised version to be published in Phys. Rev. D. The section on the Seiberg-Witten equations, which contained a sign error, has been removed. This removal leads to further issues which will appear in a future publication

References in corpus (1)

• Rational Maps, Monopoles and Skyrmions

Cited by in corpus (21)

• Creation and evolution of magnetic helicity
• The kernel of Dirac operators on ${\S }^3$ and ${\mathbb{R}}^3$
• Multiple zero modes of the Dirac operator in three dimensions
• Degeneracy of zero modes of the Dirac operator in three dimensions
• Hopf instantons in Chern-Simons theory
• Particle creation via relaxing hypermagnetic knots
• 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
• Hopf instantons and the Liouville equation in target space
• 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
• On Absence of Threshold Resonances for Schrodinger and Dirac Operators
• The zero modes and zero resonances of massless Dirac operators
• Stability of QED
• The symmetries of the Dirac--Pauli equation in two and three dimensions
• Eigenfunctions of Dirac operators at the threshold energies
• Asymptotics for Erdos-Solovej Zero Modes in Strong Fields
• Vortex Harmonic Spinors on the Nappi-Witten Space