Group Theory for Physicists (SS19)
Lecturers
Prof. Dr. Stefan Dittmaier
Dr. Philipp Maierhöfer
Dates
- Lecture: 4 hours, Mon & Wed 14-16, HS II, start: 24.04.2019
- Exercise class: 2 hours, Fri 14-16, HS II, start: 10.05.2019
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
Linear Algebra I & II, Quantum Mechanics
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 60% of the homework problems. Further details will be given in the lecture/ exercise class.
Alumni-Preis 2020