Topological solutions in gauge theory and their computer graphic representation

Abstract

A diverse range of physical phenomena, both observed and hypothetical, are described by topological solutions to nonlinear gauge field theories. Computer-generated color graphic displays can, provide a clear and detailed representation of some of these solutions, which might otherwise be physically unintelligible because of their mathematical complexity. Graphical representations are presented here for two topological solutions: (i) the solutions of a model that represents the filaments of quantized magnetic flux in a superconductor, and (ii) the solutions of an SO(3) gauge theory corresponding to a pair of separated magnetic monopoles. An introduction is provided to the gauge field theories giving rise to these solutions.