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arXiv · 1705.09632

Magnetic Zero-Modes, Vortices and Cartan Geometry

Calum Ross·Bernd Schroers
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Abstract

We show that magnetic zero-modes of the Dirac operator on $\mathbb{R}^3$ which obey an additional non-linear equation are closely related to vortex configurations on the 2-sphere, and that both are best understood in terms of the geometry induced on the 3-sphere via pull-back of the round geometry with bundle maps of the Hopf fibration. We use this viewpoint to deduce a manifestly smooth formula for square-integrable magnetic zero-modes in terms of two homogeneous polynomials in two complex variables.

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Calum Ross, Bernd Schroers. 2017-05-26. Magnetic Zero-Modes, Vortices and Cartan Geometry. https://doi.org/10.1007/s11005-017-1023-2

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