Selected Tools of Modern Theoretical Physics 2B

USOS

a projection of the E8 root lattice 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: ATTENTION, we have two differnt rooms assigned: On Mondays will be in room 422, while on Wednesdays we will meet in room 511.

Exam: We will have a written exam for this course at the end of the semester. It will take two hours. 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 or Alex.

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

Lectures

  1. A hands on introduction to Lie groups (we look at SO(3) in all detail)
    Lecture16.04.2025 10:15, notes, show recording
    Tutorial28.04.2025 09:15, exercise
  2. Mathematical preliminaries: groups, fields, vectors spaces and algebras
    Lecture23.04.2025 10:15, show recording
    Tutorial30.04.2025 09:15, exercise
  3. Invaraint tensor fields on a Lie group, transition from group to algebra
    Lecture07.05.2025 08:15
  4. Exponential map, Matrix groups
    Lecture14.05.2025 10:15
  5. Basic concepts of representation theory, adjoint representation and Killing-metric
    Lecture21.05.2025 10:15
  6. Weights, Roots, Cartan Matrix and Dynkin diagrams
    Lecture28.05.2025 10:15
  7. SU(N) representations from Young tableaux, Littlewood–Richardson rule for tensor products
    Lecture04.06.2025 10:15
  8. Action of Lie groups on manifolds, orbits, stabilizers and homogenous spaces
    Lecture11.06.2025 10:15
Based on course 14, last update on April 28th 2025, 08:03:28 | Build 738 on April 28th 2025, 08:03:44 | Times and dates shown in UTC+00:00 | Contact