
 The student understands the structure of Lie groups and Lie algebras
 The student knows the classification of semisimple Lie groups
 The student is familiar with concepts like root lattices and Dynkin diagrams
 The student knows the commonly used representations of su(n), so(n), etc
 The student has acquired competence in applying group theory methods to physics problems in mechanics, quantum mechanics and particle physics
 The student has acquired the group theoretical background underlying grand unified and supersymmetric particle physics models


Symmetries and group theoretical methods play an important role in many areas of physics, e.g., when constructing conserved quantities of a given physical system. In this course we discuss the corresponding mathematical background, studying Lie groups, Lie algebras and their representations. The examples will cover the Heisenberg algebra su(2), su(n) and the orthogonal algebra so(n). We discuss the physical relevance of these algebras with an emphasis on particle physics applications.
The course is aimed at students in both physics and mathematics, and standard for students in mathematical physics. The covered material is relevant for most courses in theoretical highenergy physics, in particular for “Quantum Field Theory”, “Particle Physics Phenomenology”, “Theoretical Foundations of Elementary Particles” and “Introduction to String Theory”.




While it is not strictly necessary to buy a textbook for this course, the following books are ighly recommended: • WuKi Tung, Group theory in Physics, World Scientific Publication, 1985 • H. Georgi, Lie Algebras in Particle Physics, Westview Press, 1999 Lecture notes will be available via blackboard. 
• 16 hours lecture • 16 hours problem session • 52 hours individual study period 
The course will be taught in English. 
Credits will be awarded based on the successful participation in the exercises (30%) and a written exam (70%) 
Classical and quantum mechanics. A background in discrete groups is recommended. 
  Required materialsReaderA complete set of lecture notes, exercises, and their solutions will be available via blackboard. 

 Recommended materialsBookWuKi Tung, Group theory in Physics, World Scientific Publication, 1985 
 BookH. Georgi, Lie Algebras in Particle Physics, Westview Press, 1999 

 Instructional modesTestsTentamenTest weight   1 
Opportunities   Block KW4, Block KW4 


 