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36051-01 - Lecture with practical courses: Group Theory and Applications (4 CP)
| Semester | spring semester 2019 |
| Course frequency | Irregular |
| Lecturers |
Stefan Antusch (stefan.antusch@unibas.ch, Assessor)
Vasja Susic (vasja.susic@unibas.ch) |
| Content | The covered topics will include: (1) Basic notions in group theory: groups, subgroups, homomorphisms, products, cosets and quotients. (2) Basic notions in representation theory: group actions and representations, irreducibility, product representations, decompositions under subgroups. (3) Representation theory of discrete (finite) groups: Schur orthogonality relations, the regular representation, classification of irreducible representations. (4) Discrete groups: basic examples, Schoenflies notation, crystallographic point groups. (5) Lie groups: examples, Lie groups and Lie algebras, exponential map, ladder operators, root and weight lattices, classification of semisimple Lie algebras, representation theory of semisimple Lie groups/algebras, SO(n) and SU(n), the Lorentz group. Applications of group theory will be demonstrated with worked out physical examples; they include consideration of symmetries in mechanical systems, in crystals from Solid State Physics, degeneracies in spectra in Quantum Mechanics, and both global and local symmetries in Particle Physics. |
| Bibliography | Example literature: [1} M. Hamermesh, "Group Theory and Its Application to Physical Problems", Dover Publications (1989). ISBN 978-0486661810. [2] J.P. Elliott and P.G. Dawber, "Symmetry in Physics: Principles and Simple Applications Volume 1", Oxford University Press (1985). ISBN 978-0195204551. and J.P. Elliott and P.G. Dawber, "Symmetry in Physics: Further Applications Volume 2", Oxford University Press (1985). ISBN 978-0195204568. [3] H. Georgi, "Lie Algebras In Particle Physics: from Isospin To Unified Theories", Westview Press 2nd Edition (1999). ISBN 978-0738202334. [4] P. Ramond, "Group Theory: A Physicist's Survey", Cambridge University Press 1st Edition (2010). ISBN 978-0521896030. [5] B. Hall, "Lie Groups, Lie Algebras, and Representations: An Elementary Introduction", Springer corrected 2nd Edition (2016). ISBN 978-3319134666. Comments: References [1] and [2] are mostly for discrete groups and applications of group theory in physics. References [3] and [4] are for Lie groups, with [4] also having some finite groups. Reference [5] is a more mathematical reference for Lie groups. |
| Language of instruction | English |
| Use of digital media | No specific media used |
| Interval | Weekday | Time | Room |
|---|
No dates available. Please contact the lecturer.
| Modules |
Module Specialisation: Physics (Master's Studies: Nanosciences) Module: Specialisation: Physics (Master's Studies: Physics) |
| Assessment format | continuous assessment |
| Assessment details | Written test (marked) |
| Assessment registration/deregistration | Reg.: course registration, dereg: cancel course registration |
| Repeat examination | no repeat examination |
| Scale | 1-6 0,5 |
| Repeated registration | as often as necessary |
| Responsible faculty | Faculty of Science, studiendekanat-philnat@unibas.ch |
| Offered by | Departement Physik |