Group Theory and Symmetries in Particle Physics

This report presents a survey of symmetries and the various applications of their mathematical framework, group theory, in modern particle physics. The text is a result of literature studies and is of introductory character, chiefly aimed at undergraduate students and graduate students with some prior knowledge of quantum mechanics, special relativity and analytical mechanics who wish to learn elementary group theory. Hence, both the pedagogical nature of the text and the physical and mathematical reasoning are of importance. The survey is illustrated in the main part of this report in form of a book, constructed in such a manner that it potentially may serve as future course literature. In the first chapters of the book, mathematical formalism is presented which is required to understand the physical theories. The latter chapters focus on physical applications, especially the classification of elementary particles according to external and internal symmetries. Finally, an overview is provided of several occurrences of these symmetries in the realm of particle physics. Moreover, a discussion regarding the challenges and opportunities of this field with a teaching aspect is conducted as an evaluation of the project