Group theory and topology in physics
The course will cover both finite groups and Lie groups, introducing key mathematical results and demonstrating applications of group theory to physical systems through many concrete examples in for instance condensed matter and particle physics. Particular attention will be paid to the construction of representations of groups which are particularly relevant for physics. The course will then introduce the notion of topology needed for the classification of topological defects and the classification of the topological phases of matter.
The course will cover:
- Finite groups and their irreducible representations
- Matrix Lie groups, Lie algebras, and their representations
- Representation theory of SU(3) and of semisimple Lie algebras
- Symmetries in quantum mechanics
- Symmetry theory of solid states (crystals) and their band structures
- Applications of group theory and topology to physical systems
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Course structure
This is a second cycle (advanced) course given during the daytime. It may be included in a master degree program, or taken as an elective course.
Teaching format
Instruction consists of lectures and exercises. The course is offered in English.
Assessment
Assessment takes place through written and oral exams.
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Schedule
The schedule will be available no later than one month before the start of the course. We do not recommend print-outs as changes can occur. At the start of the course, your department will advise where you can find your schedule during the course. -
Course literature
Note that the course literature can be changed up to two months before the start of the course.
The course literature will consist of lecture notes that are made available during the course.
In addition, the following books provide optional reading material (available as e-book via
the SU library):
M. S. Dresselhaus, G. Dresselhaus, A. Jorio,
Group Theory, Applications to the Physics of Condensed Matter
https://libris.kb.se/bib/11429675
Howard Georgi,
Lie Algebras in Particle Physics (2nd edition)
https://libris.kb.se/bib/14612978
M. Monastyrsky,
Topology of Gauge Fields and Condensed Matter
https://libris.kb.se/bib/14786157
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Contact
Teachers:
Adrien Bouhon, Nordita: adrien.bouhon@su.se
Ronnie Rodgers, Nordita: ronnie.rodgers@su.se
Academic advisor at the Department of Physics: studievagledare@fysik.su.se
Student office: studentexp@fysik.su.se
