289662 Mathematical Physics (S) (SoSe 2020)

The Mathematical Physics Seminar "Selected Topics of Symmetries in Physics" aims to convey a deeper understanding of the role and application of symmetries in particle physics.

The content is structured in two blocks: the first block is on important tools in representation theory;
the second block is about the application of those tools to the representation theory of Lie groups, in particular in the context of particle physics.

The preliminary schedule lists possible topics for seminar contributions of interested students. A seminar talk takes about 60 min.
Every topical block is by the introduced by a lecture to give some context for the more specific talks.

Topical Block I - Representation Theory and Character Theory
21.04. Introduction, Overview on Representation Theory (Unger)
28.04. Overview on Character Theory (Unger)
05.05. Topic I-1: Schur Polynomials (Participant)
12.05. Topic I-2: Young Projectors, Applications (Participant)
19.05. Topic I-3: Frobenius Formula, Recursion Formulae for Characters (Participant)
26.05. Topic I-4: Schur-Weyl Duality (Participant)

Topical Block II - Lie Groups and Algebras in Particle Physics
02.06. Overview on Lie Algebras (Unger)
09.06. Overview on Irreps on SU(N), su(N) (Unger)
16.06. Topic II-1: Roots and Weights (Participant)
23.06. Topic II-2: Casimir Operators, Applications (Participant)
30.06. Topic II-3: Haar Measure and Invariant Integration (Participant)
07.07. Topic II-4: Tensor Methods, Applications (Participant)
14.07. Topic II-5: Polynomial Representations of SU(N), Applications (Participant)

Teilnahmevoraussetzungen, notwendige Vorkenntnisse

Either Symmetries in Physics or Particle Physics

Literaturangaben

- Hermann Weyl: The Classical Groups,
Princeton University Press, 1939
- Morton Hammersh: Group Theory and its Application to Physical Problems,
Addison Wesley, 1962
- Howard Georgi: Lie Algebras in Particle Physics,
Westview Press, 1999