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

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 $\mathcal{N}=2$ 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].

arXiv comment9 pages, talk given at the XXIInd International Conference on Integrable Systems and Quantum Symmetries (ISQS-22), Prague, Czech Republic, 23-29 June 2014

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