The gauge theories for the strong and electroweak interaction have become the Standard Model of particle physics. They realize in a consistent way the requirements of quantum theory, special relativity, and symmetry principles. For the first time, we have a consistent theory of the fundamental interac­ tions that allows for precision calculations for many experiments. The Stan­ dard Model has, up to now, successfully passed all experimental tests. This success establishes the importance of gauge theories, despite the fact that gravity is not included and that the Standard Model is most likely an effec­ tive theory resulting from the low-energy limit of a more fundamental theory. The aim of this book is to present the basic ideas and concepts, the tech­ nical tools, and the predictions of the gauge theories for the fundamental constituents of matter and their interactions: Quantum Chromo dynamics for the strong interaction and the Electroweak Standard Model for the uni­ fied electromagnetic and weak interaction.

The gauge theories for the strong and electroweak interaction have become the Standard Model of particle physics. They realize in a consistent way the requirements of quantum theory, special relativity, and symmetry principles. For the first time, we have a consistent theory of the fundamental interac­ tions that allows for precision calculations for many experiments. The Stan­ dard Model has, up to now, successfully passed all experimental tests. This success establishes the importance of gauge theories, despite the fact that gravity is not included and that the Standard Model is most likely an effec­ tive theory resulting from the low-energy limit of a more fundamental theory. The aim of this book is to present the basic ideas and concepts, the tech­ nical tools, and the predictions of the gauge theories for the fundamental constituents of matter and their interactions: Quantum Chromo dynamics for the strong interaction and the Electroweak Standard Model for the uni­ fied electromagnetic and weak interaction.

Dieses Lehrbuch führt in die Theorie der Lie-Gruppen ein und ist ein unverzichtbares Werkzeug in der Quantenmechanik, bei den Eichtheorien und der Quantenchromodynamik. Die Auseinandersetzung mit mathematischen Gruppen im Rahmen der Physik ist darin begründet, dass deren algebraische Struktur zusammen mit deren Darstellungen die wesentliche Grundlage bilden, um die Eigenschaften von Symmetrien zu beschreiben. Nach grundlegenden Kapiteln über Gruppen und algebraische Darstellung wird eine umfassende Einführung in Lie-Gruppen und Lie-Algebren gegeben. Im Anschluß werden die Kenntnisse anhand der Darstellung und Berechnung weiterführender Lie-Algebren vertieft.

The gauge theories for the strong and electroweak interaction have become the Standard Model of particle physics. They realize in a consistent way the requirements of quantum theory, special relativity, and symmetry principles. For the first time, we have a consistent theory of the fundamental interac­ tions that allows for precision calculations for many experiments. The Stan­ dard Model has, up to now, successfully passed all experimental tests. This success establishes the importance of gauge theories, despite the fact that gravity is not included and that the Standard Model is most likely an effec­ tive theory resulting from the low-energy limit of a more fundamental theory. The aim of this book is to present the basic ideas and concepts, the tech­ nical tools, and the predictions of the gauge theories for the fundamental constituents of matter and their interactions: Quantum Chromo dynamics for the strong interaction and the Electroweak Standard Model for the uni­ fied electromagnetic and weak interaction.

The gauge theories for the strong and electroweak interaction have become the Standard Model of particle physics. They realize in a consistent way the requirements of quantum theory, special relativity, and symmetry principles. For the first time, we have a consistent theory of the fundamental interac­ tions that allows for precision calculations for many experiments. The Stan­ dard Model has, up to now, successfully passed all experimental tests. This success establishes the importance of gauge theories, despite the fact that gravity is not included and that the Standard Model is most likely an effec­ tive theory resulting from the low-energy limit of a more fundamental theory. The aim of this book is to present the basic ideas and concepts, the tech­ nical tools, and the predictions of the gauge theories for the fundamental constituents of matter and their interactions: Quantum Chromo dynamics for the strong interaction and the Electroweak Standard Model for the uni­ fied electromagnetic and weak interaction.

Dieses Lehrbuch führt in die Theorie der Lie-Gruppen ein und ist ein unverzichtbares Werkzeug in der Quantenmechanik, bei den Eichtheorien und der Quantenchromodynamik. Die Auseinandersetzung mit mathematischen Gruppen im Rahmen der Physik ist darin begründet, dass deren algebraische Struktur zusammen mit deren Darstellungen die wesentliche Grundlage bilden, um die Eigenschaften von Symmetrien zu beschreiben. Nach grundlegenden Kapiteln über Gruppen und algebraische Darstellung wird eine umfassende Einführung in Lie-Gruppen und Lie-Algebren gegeben. Im Anschluß werden die Kenntnisse anhand der Darstellung und Berechnung weiterführender Lie-Algebren vertieft.