Creating a database of Yang-Mills Solutions for the Differential Geometry package in Maple

Yang-Mills theory seeks to describe the behavior of elementary particles using non-Abelian Lie groups and has successfully described the unification of the electromagnetic, and weak forces as well as form a good description of quantum chromodynamics. Because of this, it is vital for understanding the Standard Model of Particle Physics. The main goal of this project is to make these solutions accessible for anyone desiring to work with and use various SU(2) Yang-Mills solutions, by creating an easily accessible database of solutions and their properties. This database will be available as a free package for the sophisticated Computer Algebra System called “Maple”. Initially the database will have 32 solutions and there are plans to continually add to this database in the future. The solutions are first input into Maple so that the Connection One-Form for each solution can be found and added to the database. Various properties presented in the paper for each solution are then tested and catalogued alongside the Connection One-Form. This project provided an opportunity for the students involved to learn valuable skills such as experience with maple, and a early introduction into Differential Geometry which is rarely seen in a undergraduate education.