GROUP34

Special Session: Lectures on Group Theory

Lectures on group theory and its applications to particle physics and condensed matter

Since 2022 will mark the 50th year of the 34th International Colloquium on Group Theoretical Methods in Physics, created in France, homeland of major front runners of group theory, such as Évariste Galois, Émile Mathieu, and Élie Cartan, we will celebrate this milestone during a special session devoted to lectures of group theory. Three lectures of 4 hours each will be organised:

1. General introduction on group theory by P. Baumann (IRMA, Université de Strasbourg) ;
   1. Examples of groups and of group actions.
   2. Representations of groups. Harmonic analysis.
   3. Correspondence Lie groups - Lie algebras.
   4. Classification of compact Lie algebras and their representations.
2. Application of group theory to particle physics by G. Bossard (École Polytechnique, France)
   1. The need for an organization principle in particle physics.
   2. The rotation group in quantum physics, addition of spins.
   3. The group SU(3) and its representations from Young diagrams. 
   4. The Gell-Mann model of quarks.
3. Application of group theory to condensed matter physics by R. Jalabert (IPCMS, Université de Strasbourg)
   1. Two and three-dimensional lattices. Reciprocal lattices and Brillouin zones.
   2. Crystal-symmetry operations.
   3. Space group. Translation and point groups.
   4. Irreducible representations of point groups.
   5. Macroscopic implications of microscopic symmetries.
   6. Electrons in solids. Bloch theorem.
   7. Crystal symmetry and the group of the k-vector.
   8. Double groups. Spin-orbit coupling.

These lectures are mainly devoted to students of Strasbourg University (PhD students as well as 1st and 2nd year Master students). No prerequisite is needed to attend these lectures.  Lectures are free of charge for students of Strasbourg University. Students are required to book their participation before [date] via [website]. For PhD students from Strasbourg these lectures are approved by the Doctoral School of Physics and Chemical-Physics (ED182) as one of the three mandatory scientific training https://edpcp.u-strasbg.fr/?p=353 and the Doctoral School Mathématiques, Sciences de l'Information et de l'Ingénieur (ED269)  http://ed.math-spi.unistra.fr/actualites/actualite/?tx_ttnews%5Btt_news%5D=23398&cHash=d044a2f2a1b4b14f64cb9bc29cd8c27f

The lectures will take place on Monday 18, Tuesday 19, Wednesday 20 and Friday 22 July 2022 from 14:00 to 18:00 at the Institut de Physique, 3-5 rue de l’Université, 67000 Strasbourg.