Symmetries of the Standard Model
J.P. Dupont (TU Delft - Applied Sciences)
Bas Janssens – Mentor (TU Delft - Analysis)
Eric Laenen – Mentor (Nikhef)
J. M. Thijssen – Graduation committee member (TU Delft - QN/Thijssen Group)
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Abstract
This thesis is divided into five parts (covering chapter 1–5), that together try to give the reader a basic understanding of the symmetries of and the mathematical structure behind the standard model. The first two chapters cover some Lie and representation theory of the Lie groups U(1), SU(2) and SU(3), which play a central role in the standard model. In the third chapter, the structure of the standard model is given, based purely on observed symmetries and (quantum numbers of) particles. In this chapter, the mathematics of the first two chapters is not used yet. In the fourth chapter, the Lie theory of chapter 1 is used to treat the gauge theory of U(1), SU(2) and SU(3), where for SU(2) also spontaneous symmetry breaking is incorporated. Finally, the fifth and last theoretical chapter gives examples of how representation theory and gauge theory can together structure the particles of the standard model and can dictate which particles and particle interactions are physically allowed. The thesis ends with some recommendations for further study of the topic at hand and for further research to symmetries beyond the standard model.