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This lecture series, held at Nish University from June to July 2010, explores the intricate world of symmetries in quantum field theory (QFT). Key topics include an introduction to groups and representations, a deep dive into Lie groups and Lie algebras, the rotation and Lorentz groups, and gauge symmetries. Additional lectures cover complex semisimple Lie algebras and Schur-Weyl duality, emphasizing their application in understanding superselection sectors and supersymmetry. A rich resource for students and researchers interested in advanced topics in theoretical physics.
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Symmetries in QFT Nish University, June - July 2010 1
CONTENT • Lecture 1 Introduction to groups and representations • Lecture 2 Lie groups and Lie algebras The rotation group Dynamical symmetry (an example) Lorentz and Poincaré groups, conformal group Groups of internal (gauge) symmetries • Lecture 3 Complex semisimple Lie algebras Schur-Weyl duality (an exercise with Young diagrams) Symmetries in QFT - superselection sectors Supersymmetry 2