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arXiv · 0808.2991

Abelian Zero Modes in Odd Dimensions

Gerald V. Dunne·Hyunsoo Min
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Abstract

We show that the Loss-Yau zero modes of the 3d abelian Dirac operator may be interpreted in a simple manner in terms of a stereographic projection from a 4d Dirac operator with a constant field strength of definite helicity. This is an alternative to the conventional viewpoint involving Hopf maps from S^3 to S^2. Furthermore, our construction generalizes in a straightforward way to any odd dimension. The number of zero modes is related to the Chern-Simons number in a nonlinear manner.

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Gerald V. Dunne, Hyunsoo Min. 2008-08-21. Abelian Zero Modes in Odd Dimensions. https://doi.org/10.1103/physrevd.78.067701

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