Resonances and bound states of the 't Hooft-Polyakov monopole

We present a systematic approach to the linearized Yang-Mills-Higgs equations in the background of a 't Hooft-Polyakov monopole and use it to unify and extend previous studies of their spectral properties. We show that a quaternionic formulation allows for a compact and efficient treatment of the linearized equations in the Bogomol'nyi-Prasad-Sommerfield limit of vanishing Higgs self-coupling and use it to study both scattering and bound states. We focus on the sector of vanishing generalized angular momentum and analyze it numerically, putting zero-energy bound states, Coulomb bound states, and infinitely many Feshbach resonances into a coherent picture. We also consider the linearized Yang-Mills-Higgs equations with nonvanishing Higgs self-coupling and confirm the occurrence of Feshbach resonances in this situation.