Representation Theory and Its Application in Particle Physics

The Lagrangian is an essential tool in the formulation of many physical theories. On the subatomic level the Lagrangian for fundamental particles is known to be symmetric under certain gauge transformations. Such transformations can be described by special unitary groups. In this project I study the representations of these groups and their associated algebras and extend them to a hypothetical tetraquark system, whose existence was recently confirmed by research conducted at the Large Hadron Collider. My results include the calculation of all the possible states of the tetraquark system in their four-fold product representation and their classification into 9 multiplets