Topological foundations of three-dimensional symmetry breaking dynamics for both Abelian and non-abelian Higgs models

We examine the role that geometrical and topological concepts have played in the recent development of theoretical physics, particularly in the areas of superstring theory and non-Abelian gauge theories. We also demonstrate the importance of these concepts for a better comprehension of the physics' dynamical laws. In this paper, we present a numerical study of the three-dimensional symmetry breaking dynamics for both non-abelian and abelian Higgs models. The non-trivial topology of the manifold of vacuum field configurations is the source of the topological excitations in the abelian Higgs model and in the other field theoretic models that will be discussed. In three-dimensional multicomponent lattice Abelian-Higgs (LAH) models minimally connected to a noncompact Abelian gauge field, we study the topological phase changes that occur in these models.