Symmetries in Physics

Lecturer:

Dr. Wolfgang Unger

unger at physik.uni-bielefeld.de

Room 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)