The interaction of isovector fermions with magnetic monopoles

The 't Hooft-Polyakov construction of a magnetic monopole is reviewed and extended to higher dimensions. Instantons are recovered as four-dimensional monopoles. Their gauge group is an obscurbed SO(4) rather than an SU(2). In the Prasad-Sommerfield limit of vanishing φ4 coupling, the classical field equations are solved producing monopole and anti-monopole solutions. The the kinetics of isovector fermions in the monopole background field are analyzed. Using supersymmetry calculation techniques, the model provides conserved supercharges in the supersymmetry limit. These charges are explicitly constructed. The spontaneous breaking of the supersymmetry identifies the breaking term and follows its implications into the final solutions of the equations of motion. The Prasad-Sommerfield limit leads to an exact classical solution of the Dirac equations in the monopole background. S-wave scattering solutions and stable fermionic monopole solutions are identified. The interactions of fermions with Dyons is solved. The thesis studies the dynamics of the broken gauge symmetry around the magnetic monopole. After spontaneous symmetry breaking, the surviving non-abelian symmetry produces a collective coordinate, called a rotator, which describes the gauge degrees of freedom of the monopole. The collective coordinate relates the incoming fermionic states to the outgoing states. The rotator dynamics leads to new conserved charges which dynamically create a rotator mass term through Schwinger terms. The rotator mass term and the fermion-rotator interaction term are combined into a shifted rotator and an effective four-fermion interaction term. The shifted rotator is formally integrated out into a perturbation expansion. The effective four-fermion interaction leads to the lowest order catalysis process. The non-abelian SU(2) symmetry and the U(1) symmetry in the direction of the HIggs field are coupled and provide equal and identical contributions to the scattering process