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

We study non-Abelian geometric phase in $\mathcal{N}=2$ 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.