| Time/place: |
Lecture
(eKVV):
Tue 10:00-12:00 (D6-135) & Fri 10:00-12:00 (D6-135)
Tutorials
(eKVV):
Group 1: Wed 12:00-14:00 (D6-135); group 2: Thu 10:00-12:00 (D6-135)
Instructor: Nicolas Borghini (borghini at physik dot uni-bielefeld dot de)
E6-123
Tutor: Steffen Feld & Dennis Schröder
Written exams: Thursday, February 22, 2018 10-13 in H6 /
Thu., March 22, 2018 10-13 in D6-135
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| Homepage: |
http://www.physik.uni-bielefeld.de/~borghini/Teaching/Symmetries
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| News: |
Results of the evaluation
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| Prerequisites: |
Classical mechanics, Special Relativity, Quantum Mechanics
(Theoretische Physik I, II)
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| Literature: |
* Cornwell: Group theory in physics
* Georgi: Lie algebras in particle physics
* Hamermesh: Group theory and its application to physical problems
* Jones: Groups, representations and physics
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| Content: |
Basics of group theory
Oct. 10 Introduction. Definition of a group
Oct. 13 & 17 Examples of groups
Oct. 17 Subgroups and cosets; conjugacy
Oct. 20 Normal subgroups; quotient groups
→ see also Normal subgroups and quotient groups by T.Gowers
Oct. 24 Direct products
Oct. 24 & Nov. 3 Homomorphisms
Representation theory
Nov. 3 & 7 Group action; definition of a group representation
Nov. 7 & 10 First examples of group representations
Nov. 10 Reducible and irreducible representations; case of finite groups
Nov. 14 Schur's lemma
Representations of finite groups
Nov. 14 Orthogonality relations for finite groups
Nov. 17 Character theory
Nov. 21 Reduction of a representation (1)
Nov. 24 Reduction of a representation (2)
Application to physical problems (1)
Nov. 21 & 24 Electric dipole; molecular vibrations
Nov. 28 Crystal field splitting
Dec. 1st Regular representation;
Representations of the symmetric group Sn
Dec. 5 Product of irreps. of the symmetric group Sn
Continuous groups
Dec. 5 & 8 Lie groups: definition and examples
Dec. 12 & 15 Lie algebras and their relation to Lie groups
Dec. 15 & 19 SO(3) and SU(2)
Dec. 19 & 22 Representations of SO(3) and SU(2)
Jan. 9 Tensor product of irreps. of SU(2); quantum-mechanical operators and rotations
Jan. 12 Wigner-Eckart theorem
Jan. 19 & 23 Representations of SU(n)
Jan. 30 Lorentz and Poincaré groups: first properties
Feb. 2 Generators and representations of the Lorentz and Poincaré groups
Application to physical problems (2)
Jan. 16 Symmetries in classical field theory
Jan. 26 Gauge field theories
Feb. 22 1st exam
(stats.)
Mar. 22 2nd exam
(stats.)
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