Hopfion solution in non-abelian gauge theory

Abstract

The purpose of this project is to study the development of a model of topological electromagnetism in empty space and to extend it further to non-Abelian theories. This topological model, which we are looking for, is based on Hopf map, a many-toone continuous function (or "map") from the S3 onto the S2, discovered by a German mathematician, Hein Hopf in 1931. In the literature survey, we have studied how such solutions (Hop on solution) were constructed via Bateman's and Ranada's construction. Some attempts have been made to construct Hop on solutions in SU(2) Yang-Mills theory. An ansatz has been made by taking a analogy similar to Ranada's construction. This approach has shown to be a promising candidate for such type of solution in SU(2) Yang-Mills theory. iii