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Group Theory for Physicists (SS23)

Lecturer

Prof. Dr. Stefan Dittmaier
Exercise class: Dr. Maximilian Stahlhofen

Dates

  • 4 hours, Mon 14-16 (Hörsaal II) and Fri 12-14 (Hörsaal II).
  • Exercise class: 2 hours, Wed 12-14 (Seminarraum II/III).

ILIAS Link

To get access to the ILIAS page please register for the lecture in HISinOne. Your registration will be transferred to ILIAS automatically (usually over night).

Target Audience

  • BSc students ("Wahlpflichtmodul")
  • MSc students ("Elective subject")

Content

  • Basic concepts and group theory in QM
    (Symmetry transformations in quantum mechanics, group-theoretical definitions, classes, invariant subgroups, group representations, characters, (ir)reducibility, Schur's lemmas)
  • Finite groups
    (unitarity theorem, orthogonality relations, classic finite groups, applications in physics)
  • SO(3) and SU(2)
    (basic properties, relation between SO(3) and SU(2), irreducible representations, product representations and Clebsch-Gordan decomposition, irreducibletensors,Wigner-Eckart theorem)
  • SU(3)
    (basic properties, irreducible representations, product representations, applications in the quark model of hadrons)
  • Lie groups
    (basic properties, Lie's theorems, Lie algebra, matrix representations and exponentiation)
  • Semisimple Lie groups and algebras
    (basic concepts, Cartan subalgebra, Cartan-Weyl and Chevalley bases, root systems, classification of complex (semi)simple Lie algebras, Dynkin diagrams, finite-dimensional representations, a glimpse on applications in theories of fundamental interactions in particle theory)
  • Lorentz and Poincare groups and algebras
    (basic properties, finite-dimensional and infinite-dimensional representations, method of induced representation, application to particle states)

Prerequisites

Quantum Mechanics (Theoretical Physics III), Linear Algebra

Literature

  • R.N. Cahn, "Semi-Simple Lie Algebras and Their Representations", Dover Publications.
  • R. Campoamor-Stursberg, M. Rausch de Traubenberg, "Group Theory in Physics", World Scientific.
  • R.W. Carter, "Finite Groups of Lie Type: Conjugacy Classes and Complex Characters", Wiley Classics Library, Wiley.
  • J. Fuchs, C. Schweigert, "Symmetries, Lie Algebras & Representations: A Graduate Course for Physicists", Cambridge University Press.
  • H. Georgi: "Lie Algebras in Particle Physics", Westview Press.
  • R. Gilmore, "Lie Groups, Lie Algebras, and Some of Their Applications", Dover Books on Mathematics.
  • B.C. Hall, "Lie Groups, Lie Algebras, and Representations", Springer.
  • M. Hamermesh: "Group Theory and Its Application to Physical Problems", Dover Publications.
  • P. Ramond, "Group Theory: A Physicist’s Survey", Cambridge University Press.
  • W.-K. Tung: "Group Theory in Physics", World Scientific.
  • B.G. Wybourne, "Classical groups for physicists", Wiley.
  • A. Zee, "Group Theory in a Nutshell for Physicists", Princeton University Press.

Requirements for Course Achievement ("Studienleistung")

Active and regular participation in the tutorials, including solutions to 50% of the homework problems. Further details will be given in the lecture/tutorials.

Lecture Notes & Exercise Sheets

see ILIAS page.
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