Master’s studies

Syllabus for Symmetry and Group Theory in Physics

Symmetri och gruppteori


  • 5 credits
  • Course code: 1FA353
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Physics A1N
  • Grading system: Fail (U), 3, 4, 5
  • Established: 2010-03-18
  • Established by: The Faculty Board of Science and Technology
  • Applies from: week 31, 2010
  • Entry requirements: 120 credits with Quantum Physics or equivalent. Nuclear Physics, Particle Physics and Solid State Physics are recommended.
  • Responsible department: Department of Physics and Astronomy

Learning outcomes

On completion of the course, the student should be able to

  • apply symmetry considerations and group theory to solve problem within molecular physics, solid state physics and particle physics

  • analyse both discrete and continuous symmetries of physical systems using group theoretical tools

  • analyse properties of physical systems, such as transition probabilities, by means of representations

  • use Young tableaux, Clebsch-Gordan decomposition and Wigner-Eckart theorem in calculations

  • apply representation theory and decompose into irreducible representations

  • calculate Casimir operators for Lie groups, construct their root and weight diagrams and calculate roots and weights


The course gives a general introduction to the description of symmetry properties of physical systems. Group theory and the theory of group representations. The Wigner-Eckart theorem. Young tableaux. Discrete groups: point groups, space groups and the permutation group with applications within molecular and solid state physics. Continuous groups and Lie algebra with applications within particle physics, such as the special unitary groups and the Lorentz and Poincaré the groups. General treatment of Lie groups.




Homework assignments.

Reading list

Reading list

Applies from: week 32, 2010

  • Jones, H.F. Groups, Representations and Physics

    Taylor & Francis,

    Find in the library


  • Tinkham, Michael Group theory and quantum mechanics

    Mineola, N.Y.: Dover Publications, 2003

    Find in the library