Humboldt Universitaet zu Berlin Faculty of Mathematics and Natural Sciences Department of Chemistry auf deutsch

4020250027 Group theory in Physics       

Präsenzkurs

classroom language

EN

aims

Students learn about the theory of Lie groups and Lie algebras and can apply this in the context of elementary particle physics and quantum field theory. Note that every second week, the lecture is replaced by an exercise class.

requirements

Solid knowledge of linear algebra and multivariable calculus. Knowledge of quantum physics is helpful when discussing applications in physics.

This masters level course could also be accessible to and useful for advanced bachelors students.

structure / topics / contents

Structure of groups, finite groups, Lie groups, representations of groups, group theory and quantum mechanics, applications in molecular physics and solid state physics, Lie algebras, 3-dimensional rotation groups, semisimple complex Lie algebras, semisimple real Lie algebras, classical Lie algebras (su(n), so(n), sp(2n)), Representations of Lie algebras, roots and weights, Dynkin diagrams, Young diagrams, characters, classification of Lie algebras, exceptional algebras, Lorentz-Poincaré and conformal algebras and groups, applications in the theory of elementary particles and quantum field theory, Lie superalgebras and supergroups, infinite-dimensional Lie algebras.

assigned modules

P25.1.b

amount, credit points; Exam / major course assessment

4 SWS, 6 SP/ECTS (Arbeitsanteil im Modul für diese Lehrveranstaltung, nicht verbindlich)
Written exam (3 hours maximum) or oral exam (30 min maximum)

literature

Brian C. Hall. Lie Groups, Lie Algebras, and Representations. Springer