This is the mandatory Selected tools of modern theoretical physics 2B course of the Master in Theoretical Physics at the University of Wrocław. It is tailored towards master and (if interested) PhD students who are familiar with

• linear algebra,
• analysis, and ideally
• differential geometry (from Selected Tools of Modern Theoretical Physics 2A).

There are many good books on the subject, four that I would like to point out are

• Fecko: Differential Geometry and Lie Groups for Physicists
• Naimark, Štern: Theory of Group Representations
• Barut, Rączka: Theory of Group Representation and Applications
• Zee: Group Theory in a Nutshell for Physicists

There will be 2 hours of lectures and 2 hours of labs each week. Note that we will start in the middle of the semester, after part A of this course which deals with differential geometry. Exercises will be posted here a week before the lab they are discussed in. Please keep in mind that active participation in the labs and especially submitting the solution to the posed problems is important to pass the course. M.Sc. Alex Swash will be the assistant for this course. Please fell free to contact him or me if you have any questions. For information about credits points, please refer to the syllabus or contact me directly.

Location: We will be in room 403 for both, the lecture and the tutorials

Exam: We decided together that the written exam for this course will take place on Monday, the 29th of June 2026, at 11:00 in room 403. It will take two hours (120 minutes) and we will discuss a practice exam in the last tutorial to help you preparing for it. Please be there five minutes earlier such that we can start on time. Also note that you need to have more than 50% of the points from the exercises assigned to you to qualify for the exam. You can check your points here on the website, or, if you are in doubt, with me.

Additional material for the individual lectures, including the exercises which we discuss in the labs, is given below: