Symmetries in Physics


Lecturer:

     Dr. Wolfgang Ungerunger at physik.uni-bielefeld.deRoom E6-118

Lecture:

Tue. 10:15-11:45 in Room D6-135

Lecture:

Thu. 10:15-11:45 in Room C01-142

Exercises:

(Giuseppe Gagliardi)    Mo. 14:15-15:45 in Room U2-135

Content:

Group Theory
Representation Theory
Discrete Groups
Lie Groups, Poincare Groups
Applications

Prequisites:

Course in Quantum Mechanics is helpful

Lectures: (preliminary, subject to change)

The lecture notes will be published successively after each lecture. The script can be downloaded here

Lecture 1 (9. Oct. '18): Introduction: The many faces of symmetries

Lecture 2 (11. Oct. '18): Introduction: Role of Symmetries in Physical States and Laws

Lecture 3 (16. Oct. '18): Group Axioms, Group Properties, Group Presentations

Lecture 4 (18. Oct. '18): Homomorphisms, Isomorphism

Lecture 5 (23. Oct. '18): Subgroups, Normal groups

Lecture 6 (30. Oct. '18): Conjugacy Classes

Lecture 7 (6. Nov. '18): Direct Products

Lecture 8 (8. Nov. '18): Discrete Groups (1)

Lecture 9 (13. Nov. '18): Discrete Groups (2)

Lecture 10 (15. Nov. '18): Continuous Groups: Rotations

Lecture 11 (20. Nov. '18): Continuous Groups: Euclidean Group

Lecture 12 (22. Nov. '18): Lie Group

Lecture 13 (27. Nov. '18): Lie Groups Algebras

Lecture 14 (29. Nov. '18): Matrix Lie Groups

Lecture 15 (4. Dec. '18): The Galielei Group

Lecture 16 (6. Dec. '18): The Lorentz Group

Lecture 17 (11. Dec. '18): The Poincare Group

Lecture 18 (13. Dec. '18): Classical Field Theoris

Lecture 19 (18. Dec. '18): Noether Theorem, Conserved Charges

Lecture 20 (20. Dec. '18): Representation Theory: Basics

Lecture 21 (8. Jan. '18): Redcible and Irreducible Representations

Lecture 22 (10. Jan. '19): Characters

Lecture 23 (15. Jan. '19): Character Tables, Schur's Lemma

Lecture 24 (17. Jan. '19): Orthogonality Relations

Lecture 25 (22. Jan. '19): Irreps of the Symmetric Group

Lecture 26 (24. Jan. '19): Irreps of U(1)

Lecture 27 (29. Jan. '19): Irreps of SU(2)

Lecture 28 (31. Jan. '19): Irreps of SU(3), SU(N), Application to QCD


Exercises:

To qualify for the written exam (you can earn 10 CP)
you need to get 50% of the points from the homework.

The points of each sheet sum up to 20 points.

The exam takes place on Feb. 15th, 10 am in H10.

The retry exam takes place on March 18th, 10 am in H10.

The exercise that is marked on the exercise sheet should be handed in prior to the tutorial on mondays.
The tutor will discuss the solutions immediately, hence we cannot accept solutions after this deadline.

           
   Amalie Emmy
Noether

Sheet 1
(Noether Theorem)
              Niels Hendik Abel

Sheet 2
(Abelian Group)
               Joseph-Louis
Lagrange

Sheet 3
(Lagrange Theorem)
     
   Arthur Cayley

Sheet 4
(Cayleys Theorem)
               Evariste Galois

Sheet 5
(Galois Theory)
               Camille Jordan

Sheet 6
(Jordan-Hoelder Theorem)
     
   Euclid of Alexandria

Sheet 7
(Euclidean Group)
               Sophus Lie

Sheet 8
(Lie Group)
               Elie Cartan

Sheet 9
(Cartan Theorem)
           
     
   Hendrik A. Lorentz

Sheet 10
(Lorentz Transformation)
               Henri Poincare

Sheet 11
(Poincare Group)
               Issai Schur

Sheet 12
(Schur's Lemma)
           
     
   Ferdinand Georg Frobenius

Sheet 13
(Irreps of S_n, A_n)
           

Literature:

Books:

H.F. Jones, Groups, Representations and Physics, Taylor & Francis 1998.

J.F. Cornwell, Group Theory in Physics, Vol. I and II, Academic Press 1984.

W. Ludwig and C. Falter, Symmetries in Physics, Springer 1995.

H.Georgi, Lie Algebras in Particle Physics, Reading, Benjamin 1982.

W.K. Tung, Group Theory in Physics, World Scientific, 1985.

Skripts:

Andreas Wipf, Uni Jena

Nicolas Borghini, Uni Bielefeld

Mikko Laine, Uni Bern


External Links:

Natural Patterns: https://ecstep.com/natural-patterns

GAP (Groups, Algorithm, Programming): https://www.gap-system.org/ <


Last modified: Tue Oct 15 18:50:44 CET 2013