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arXiv · 1409.8238

Supersymmetry and non-Abelian geometric phase for a free particle on a circle with point-like interactions

Satoshi Ohya
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Abstract

Though not so widely appreciated in the literature, supersymmetric quantum mechanics provides an ideal playground for studying non-Abelian geometric phase, because supersymmetry always guarantees degeneracies in energy levels. In this paper we first present a simple supersymmetric model for a free particle on a circle with point-like interactions that exhibits $\mathscr{N} = 2$ supersymmetry and doubly degenerate energy levels. We then show that Berry's connection in this model is given by the Wu-Yang-like magnetic monopole in SU(2) Yang-Mills gauge theory. This article is largely based on our recent work [arXiv:1406.4857].

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Satoshi Ohya. 2014-09-29. Supersymmetry and non-Abelian geometric phase for a free particle on a circle with point-like interactions. https://doi.org/10.1088/1742-6596/563/1/012021

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