The exact solution is presented for the classical and quantum mechanical problem of a spinless, isospin-carrying test particle interacting with a singular monopole of the same large-distance asymptotic behaviour as the Prasad-Sommerfield 1-monopole. It is demonstrated that this problem has a dynamical O(4) symmetry. The classical mechanical equation of motion is traced back to a non-relativistic Coulomb problem. The long-range Higgs field results in monopole-test-particle bound states. The bound state spectrum is derived on a purely group theoretic basis using dynamical symmetry.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics