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

22nd International Conference on Integrable Systems and Quantum Symmetries

Ohya, Satoshi^1,2

Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Pohraniní 1288/1, Dín

40501, Czech Republic^1

Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University in Prague, Behová 7, Prague

11519, Czech Republic^2

关键词: Free particles;    Gauge theory;    Geometric phase;    Magnetic monopoles;    Supersymmetric models;    Supersymmetric quantum mechanics;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/563/1/012021/pdf
DOI  :  10.1088/1742-6596/563/1/012021

来源: IOP

【 摘 要 】

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 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 [1].