Symmetry in Condensed Matter Physics

Part 1:

Theory of groups and their representations (Paolo G. Radaelli)

Part 2:

Molecular vibrations and selection rules, rotational symmetry of spin and orbital states, crystal field effects, translational symmetry and electron/phonon dispersion relations (Radu Coldea)

Lecture 1-8 Lecture Notes

• Handouts[pdf] (revised on 12 Nov 2019)

Lecture Slides

• Lecture 1[pdf]
• Lecture 2[pdf]
• Lecture 3[pdf]
• Lecture 4[pdf]
• Lecture 5[pdf]
• Lecture 6[pdf]
• Lecture 7[pdf]
• Lecture 9 Molecular Vibrations [pdf]
• Lecture 10 IR and Raman selection rules[pdf]
• Lectures 11 and 12 rotational symmetry [pdf]
• Lectures 13 and 14 translational symmetry [pdf]

Problem Sheets

• Problem Sheet 1[pdf]
• Problem Sheet 2[pdf]
• Problem Sheet 3[pdf]
• Problem Sheet 4[pdf]
• Problem Sheet 5[pdf]

Point-Group Character Tables

• Character Tables[pdf]

Additional material

• A very useful paper on "How to read (and understand) the International Tables of Crystallography - Volume A"[pdf]
• Representations of the full rotation group SO(3)[pdf]
• A short clip where Hans Bethe explains the application of group theory to crystals

Suggested readings

• M.S. Dresselhaus, G. Dresselhaus and A. Jorio, Group Theory - Application to the Physics of Condensed Matter, Springer-Verlag Berlin Heidelberg (2008).
• V. Heine, Group Theory in Quantum Mechanics, Dover (2007)
• F.J. Nye, Physical Properties of Crystals, Oxford Science Publications, Oxford University Press (1957)