• solitons
• monopole
• vortex
• hypergeometric functions
• gauge theory
• topological obstruction
• dirac string

The main objectives of this thesis are to investigate the relationship between the scattering of boson fluctuations on a fixed monopole in a non-abelian theory (SU(3)) and the topological obstructions that restrict the possible zero modes of the monopole. The SU(3) solution is obtained by embedding the SU(2) solution, but the embedding is not uniquely defined and can be altered by a singular gauge transformation. This freedom introduces bosonic fluctuations, which reside on a CP1 moduli space. However, explicit solutions of the linearized equation for these bosons yield wave functions that are not normalizable, indicating that the particles arising from these fluctuations are not physically meaningful. By examining the scattering solutions in the same color direction as the zero modes, we derive explicit solutions expressed in terms of hypergeometric functions. These solutions do not conserve charge or helicity. When studying the scattering of fermions on an Abelian monopole, we encounter a similar issue where the solutions involve exciting the orientational zero modes, transforming the monopole into a dyon that has an additional electric charge. For SU(3) the existence of chromodyons is not possible due to the inability to excite the fluctuations, resulting in a persisting problem. We demonstrate how the non-existence of these modes is a consequence of the presence of the Dirac string in the singular gauge, which prevents a definition of a global color gauge group.