Symmetrien, Teilchen und Felder

Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects like elementary particles. The present work discusses aspects of relativistic quantum field theory as the mathematical theory of particle physics which are relevant for the modern description of elementary particles and their associated fields hitherto considered as fundamental building blocks of the theory. Due to the abstract nature of quantum field theory, these aspects can only be touched by their exemplification within a review.