Group Theory in Condensed Matter: A Practical Introduction.

By Prof. Juan Luis Mañes Palacios, departamento de Física de la Materia Condensada, Facultad de Ciencia y Tecnología, EHU, Bilbao.

September 2017.


This course gives a practical introduction to the uses of group theory in actual condensed matter problems. The stress is on applications rather than formalism, and the main ideas and techniques in group theory will be introduced through practical examples. No previous knowledge of group theory is assumed.


8 lectures of 90 minutes each (2 lectures per week) from 11h30 to 13h00 on September 5th, 6th, 11th, 13th, 18th, 20th, 25th, 27th.


1. Introduction: Symmetries, degeneracies and representations.
2. Irreducible representations as building blocks. Application to molecular vibrations.
3. Operations with representations I: Physical properties and spectra.
4. Operations with representations II: IR and Raman activity. Selection rules.
5. Spin and double valued representations. Splitting of atomic orbitals in crystals.
6. Space groups and their representations. Symmorphic and non-symmorphic space groups.
7. Associating irreducible representations to electron and phonon bands. Compatibility relations. 
8. Group theory and topology.

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