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Wavefunctions for Non-Abelian Vortices

Kai-Ming Lee·Hoi-Kwong Lo
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Abstract

We construct exact wavefunctions of two vortices on a plane, a single vortex on the cylinder and a vortex on the torus. In each case, the physics is shown to be equivalent to a particle moving in a covering space, something simple to solve in those examples. We describe how our solutions fit into the general theory of quantum mechanics of $N$ particles on a two-dimensional space and attribute our success to the fact that the fundamental groups are Abelian in those simple cases that we are considering.

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Kai-Ming Lee, Hoi-Kwong Lo. 1997-01-18. Wavefunctions for Non-Abelian Vortices. https://arxiv.org/abs/hep-th/9505108

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