2010/12/15 by Katie M Russell, K. M. Russell, Bernd J. Schroers +1 · 6 citations
Mathematics · Physics and Astronomy · #Bound state #Magnetic monopole #Mathematical physics #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Spectral Theory in Mathematical Physics #Theoretical physics #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.83.065004
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 83(6) (American Physical Society) · 33 pages, 7 figures
arxiv created 2010/12/15 · openalex publication_date 2011/03/02 · arxiv updated 2011/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.