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arXiv · 1012.3438

On resonances and bound states of the 't Hooft-Polyakov monopole

Katie M Russell·Bernd J Schroers
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Abstract

We present a systematic approach to the linearised 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 linearised equations in the BPS limit of vanishing Higgs self-coupling, and use it to study both scattering and bound states. We focus on the sector of vanishing generalised angular momentum and analyse it numerically, putting zero-energy bound states, Coulomb bound states and infinitely many Feshbach resonances into a coherent picture. We also consider the linearised Yang-Mills-Higgs equations with non-vanishing Higgs self-coupling and confirm the occurrence of Feshbach resonances in this situation.

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Katie M Russell, Bernd J Schroers. 2010-12-15. On resonances and bound states of the 't Hooft-Polyakov monopole. https://doi.org/10.1103/physrevd.83.065004

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