Group Theory in Physics

Graduate course, 5 points, March-May 2007

The goal of the course is to give an introduction to the use of group theory in physics. After the course the students will be familiar with the concept of symmetry groups and their representations. The student will be able to apply group theory on the physics of molecules, solids and elementary particles.

Starting date: Tuesday March 27, Room 11167, 15-17

Prerequisities: Quantum Mechanics, advanced course or equivalent

Contents:

Fundamental concepts and representations
Point groups and the Permutation group
Rotation groups
Space groups
Applications to spectroscopy
Lie algebras
Continuous groups
Applications to the quark model and colour

Lecture Notes:
The lecture notes of the first part of the course which are compiled by Johan Bläbäck (under GPL-licence) has been checked by the lecturer (Lars Nordström) and can be obtained in pdf format here or as latex-source here. The lecturer takes all responsibility for any errors.

The partial lecture notes of the second part of the course which are compiled by Johan Bläbäck (under GPL-licence) has been checked by the lecturer (Johan Rathsman) and can be obtained in pdf format here or as latex-source here. The lecturer takes all responsibility for any errors.

Projects:
The list of projects together with some more information can be found here.

Litterature:
There will be no particular book for the course. Instead the following general books on group theory are recommended. (If you want to have a look at one of the books please feel free to contact one of the lecturers.)

"Group Theory in Physics, An Introduction", J.F. Cornwell, Academic Press. (A bit more formal and not so much material on applications. Quite expensive.)
"Symmetries in Physics: Group Theory Applied to Physical Problems", W Ludwig and C Falter, Springer Series in Solid-State Sciences. (Unfortunately out of print.)
"Symmetry in Physics (vol 1 and 2)", JP Elliot and PG Dawber, Palgrave Macmillan. (Unfortunately out of print.)
"Groups, Representations and Physics", HF Jones, Taylor & Francis. (More intuitive presentation. Covers most but not all of the course contents. Not so expensive.)
Useful material on group theory in particle and nuclear physics may also be found in the following books
"Lie Algebras in Particle Physics", H. Georgi, Westview Press
"Quantum Mechanics: Symmetries", W. Greiner and B. Müller, Springer
"Elementary Particle Physics", O. Nachtmann, Springer
"Gauge Theory of Elementary Particle Physics", Cheng and Li, Oxford
"Introduction to Symmetries", I. Aitchison, lecture notes, http://www-thphys.physics.ox.ac.uk/users/IanAitchison/home.html
Useful material on group theory in the physics of molecules and solids may also be found in the following books
Band Theory of Solids: An Introduction from the Point of View of Symmetry, SL Altman (Oxford Science Publications, Clarendon Press)
"Symmetri", Jean-Louis Calais med tillägg av Leif Karlsson mfl, Symmetri.pdf (Unfortunately only available in Swedish)

Links to point group character tables: http://www.mpip-mainz.mpg.de/~gelessus/group.html

and to information about space groups: http://www.cryst.ehu.es/

The course gives 5 points, and the examination will be in the form of hand-in excercises and project, on a specialized subject, by each of the participants.

Lecturers:
Lars Nordström, Lars.Nordstrom[at]fysik.uu.se, 018-4717309.
Johan Rathsman, Johan.Rathsman[at]physics.uu.se, 018-4713049

Preliminary schedule:
Date Time Place Subject Lecture-Notes Hand-in exercise
Tue 27/3 15-17 11167 Fundamental concepts Groups Nr. 1
Thu 29/3 15-17 12167 Fundamental concepts, cont'd
Tue 17/4 10-12 11167 Representations Nr. 2
Thu 19/4 13-15 11167 Representations, cont'd
Tue 24/4 13-15 80109 Point groups and applications Nr. 3
Thu 3/5 15-17 11167 Space groups
Tue 8/5 10-12 12167 Spectroscopy Nr. 4
Thu 10/5 10-12 12167 Lie Algebras Nr. 5
Wed 16/5 13-15 80109 Lie Algebras and SU(2)
Tue 22/5 15-17 11167 SU(2) cont'd Nr. 6
Thu 24/5 10-12 12167 Roots and Weights
Mon 28/5 13-15 12167 Roots and Weights and SU(3) Nr. 7
Thu 31/5 13-15 12167 SU(3) and Lorentz group Nr. 8
Tue 5/6 13-15 12167 Presentation of projects
Thu 7/6 10-12 12167 Presentation of projects

Presentations by students (10+5 min):
Students Topic Presentation Report
Moritz and Stefan Young Tableaux pdf-file pdf-file
Pelle and Anders Symmetry in Spectroscopy pdf-file pdf-file
Johan Supersymmetry pdf-file pdf-file
David and Henrik P Chiral Perturbation Theory pdf-file
Henrik JMass relations pdf-file
David and Patrik Double groups pdf-file pdf-file
Erik and Peder SU(5) pdf-file pdf-file
Carl-Oscar Exotic hadrons pdf-file
MaciekColour Groups - pdf-file