A Investigation of a Class of Self-Dual Monopole Solutions.

The object of this investigation is to exhibit explicit magnetic monopole solutions of the grand unified field equations for different gauge groups. Chapter 1 introduces the assumptions used to simplify the field equations. The class of grand unified models considered contains gauge fields and a single Higgs field in the adjoint representation. The solutions sought are spherically symmetric, and the Bogomolny-Prasad-Sommerfield limit is assumed. Physically important finite energy solutions must satisfy boundary conditions at the origin and in the far-field. In Chapter 2, the spherical symmetry is implemented by a particular type of imbedding, known as maximal imbedding. The general solution of the field equations in this case is known, and the integration constants are chosen to match the boundary conditions using the Laplace transform. Chapters 3 and 4 investigate the existence and stability of the related McGlinn solutions.