08.128.733 Symmetries in Physics

Instructors: apl. Prof. Dr. Georg von Hippel

Event type: Lecture/practice class

Displayed in timetable as: 08.128.733

Hours per week: 4

Credits: 6,0

Language of instruction: Englisch

Min. | Max. participants: - | -

Requirements / organisational issues:
Knowledge of Linear Algebra, classical field theory and (non-relativistic) Quantum Mechanics is expected.
 

Contents:

1. Mathematical foundations: Groups and their properties, representations of groups, irreducible representations, Schur's lemmas, character tables, Clebsch-Gordan decomposition, Lie groups and Lie algebras, root systems and Dynkin diagrams, Young tableaux
   
2. Physical applications: Noether's theorem, SO(3) and SU(2) for spin and isospin, Wigner-Eckart theorem, SO(4) and the Runge-Lenz vector, SU(3) and the "eightfold way", Poincaré group and relativistic particles, discrete symmetries
   
3. Local symmetries: electromagnetism as a gauge theory, non-abelian gauge theories
   
4. Broken symmetries: Goldstone's theorem, Higgs effect, anomalies in QFT
   

Recommended reading list:

1. S. Scherer, Symmetrien und Gruppen in der Teilchenphysik (Springer Spektrum, 2016)
   
2. H.F. Jones, Groups, Representations and Physics (IoP Publishing, 1998)
   
3. A. Zee, Group Theory in a Nutshell for Physicists (Princeton University Press, 2016)
   

Digital teaching:
It is planned to hold the lectures entirely in person, while offering a hybrid course on ILIAS as a supplement; this would enable a shiftover to online teaching if and when required.