Lectures (weekly, start Wednesday 20.04.2022)
Wedesdays 16:15 - 17:45, Building 3701 (ITP), Room 268 (großer Seminarraum)
Thursdays 08:15 - 09:45, Building 3701 (ITP), Room 269 (kleiner Seminarraum)
An interactive site map for all lecture- and seminar-rooms can be found here.
Exercises (every 2nd week Thursdays, start 28.04.2022)
Thursdays 08:15 - 09:45, Building 3701 (ITP), Room 269 (kleiner Seminarraum).
In the weekly extercise classes we will present and discuss the solutions of the problems on the sheet that was distributed here on the week before. Students are expected to present their solutions upon request or register for their presentation beforehand.
Stucture
The Lecture is structured into (3+1) hours weekly, meaning that there are 2 lectures of 90 minutes each on Wednesday and Thursday in odd weeks and one lecture and one exercise of 90 minutes each in even weeks.
Certificates of study and examination (Studien- und Prüfungsleistung); module assignments; ECTS points
An ungraded certificate of study (Studenleistung) will be given to participating students depending on their performance in the problem-solving classes. This includes a complete and correct presentation of at least one problem. In addition, a graded certificate of examination (Prüfungsleistung) will be given after an individual oral examination of about 40 minutes. This lecture can exclusively account for either the BSc-module "moderne Aspekte der Physik" (1601) or for the MSc-module "Ausgewählte Themen moderner Physik" (1621). The number of ECTS points for this lecture is 5 (one for each weekly hour - 45 minutes - of lectures and two for exercises).
Prerequisites
Linear algebra, special relativity, quantum mechanics.
Preliminary list of topics
- Finite dimensional Lie algebras.
- Finite dimensional (matrix) Lie groups.
- Universal cover group; examples.
- The Lorentz and Poincaré groups, their universal covers, and their Lie-algebras.
- Contraction and deformation of Lie-algebras. Relation of Galilei and Lorentz groups.
- SU(2) and SL(2,ℂ) spinors.
- Real Lie-algebras and their complexification.
- Weyl's unitarity-trick.
- Tensor algebra for SL(2,ℂ) spinors and the classification of finite-dimensional irreducible representations of SL(2,ℂ).
- Unitary irreducible representations of the Poincaré group and linear wave equations.
Lecture Notes
My handwritten personal notes (in german) can be read and downloaded here (Part 1 is headed "Lecture 2, Part 2 "Lecture 3" etc.; there is no "Lecture 1"):
Textbooks and other texts
Here are some suggestions for further reding:
- Roman Sexl und Helmuth Urbantke: Relativity, Groups, Particles. Special Relativity and Relativistic Symmetry in Field and Particle Physics. Springer Verlag, Wien (2001).
- James E. Humphreys: Introduction to Lie Algebras and Representation Theory. Springer Verlag, New York (1972).
- Brian C. Hall: Lie Groups, Lie Groups, Lie Algebras, and Representations. Springer Verlag, New York (2003).
- Domenico Giulini: Algebraic and geometric structures of Special Relativity.
