COURSE FY8104
Application of Symmetry Groups in Physics
Fall 2009
- Purpose:
The aim of this course is to give an introduction to
group theory and some of its applications in physics.
The course is lectured every second year.
- Teacher: Jan Myrheim,
E5-102, Lars Onsagers Hus (aka Realfagbygget), tel. 73 59 36 53
- Recommended text book:
Michael Tinkham: Group Theory and Quantum Mechanics.
This book from the 1960s exists in Dover edition
at about Nkr 200
- Notes
These are notes, unfortunately not quite complete.
You are not required to read these notes from beginning to end.
But I hope that you will find useful reading here if you want to learn
and understand more of the mathematics than is covered in the lectures.
Table of contents
(ps file or
pdf file).
Part I: Transformation groups and basic group theory
(ps file or
pdf file).
Part II: Linear representations of groups
(ps file or
pdf file).
Part III: Introduction to Lie groups
(ps file or
pdf file).
Part IV: Appendices
(ps file or
pdf file).
Part V: Representations of the symmetric group S_n
(ps file or
pdf file).
- Contents (of previous years, may change somewhat this year):
Classes, cosets, factor groups. Irreducible and reducible representations. The character of
a representation. Point groups and product groups. Invariant tensors. Symmetry of the
Hamilton operator and corresponding perturbation term. Calculation of matrix elements.
Crystal field splitting. Optical spectra. Magnetic space groups. Ginzburg-Landau theory.
Selection rules. Hybridization. Lattice vibrations. Symmetry of energy bands in electrons.
Continuous groups and Lie groups.
- Lectures (4 hours/week):
Monday 10:15-12 and Wednesday 08:15-10 in E5-103.
- Examination set 2007
In Norwegian
(ps file or
pdf file).
In English
(ps file or
pdf file).
Solutions, in Norwegian
(ps file or
pdf file).
- Examination set 2009
In English
(ps file or
pdf file).
Solutions, in English
(ps file or
pdf file).
- Exam:
Written exam on Wednesday, December 9, 2009.