Non-Abelian Monopole in the Parameter Space of Point-like Interactions

TL;DR

This paper explores the non-Abelian geometric phase in supersymmetric quantum mechanics, revealing that the Berry connection corresponds to an $SU(2)$ magnetic monopole, linking quantum mechanics with topological monopole structures.

Contribution

It demonstrates that the non-Abelian Berry connection in a supersymmetric quantum system is equivalent to the $SU(2)$ magnetic monopole, connecting geometric phases with topological monopole configurations.

Findings

Non-Abelian Berry connection matches $SU(2)$ magnetic monopole.

Supersymmetric quantum mechanics exhibits non-Abelian geometric phases.

Connection to monopole structures in quantum parameter space.

Abstract

We study non-Abelian geometric phase in $\mathscr{N} = 2$ supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry's connection is that of $SU(2)$ magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule.