Scheme for Building a ’t Hooft–Polyakov Monopole

Abstract

We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered exponential of the smooth SU(2) 't Hooft-Polyakov monopole. We further show that, by adjusting a potential on the sphere, the monopole becomes a Bogomol'nyi-Prasad-Sommerfield monopole and obeys the Bogomol'nyi equations.