Course Code : | 1003WETIGR |

Study domain: | Physics |

Academic year: | 2019-2020 |

Semester: | 1st semester |

Sequentiality: | Credit for Mathematical methods for physics I, II & III, General physics I & II, Experimental physics I, computer practicum, Intro analytical mechanics and Intro to chemistry |

Contact hours: | 30 |

Credits: | 3 |

Study load (hours): | 84 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | David Eelbode |

At the start of this course the student should have acquired the following competences:

an active knowledge of

an active knowledge of

- Dutch

- English

Basic knowledge mathematics (linear algebra and multivariate calculus)

- You known what groups are (both finite and infinite of Lie-type) and you can provide examples from physics.
- You know the definitions of sub- and quotient groups and properties thereof.
- You can explain the topological properties of the spin group and the orthogonal group.
- You know what a Lie algebra is, and you can work with the exponential map to relate it to the corresponding group.
- You know what representations for Lie groups or Lie algebras are, and you can describe the spin representations for SU(2) and sl(2) in detail.
- You can explain what 'weights' and 'roots' are, where the Lie algebra sl(3) can be used as a relevant example to illustrate these notions.

The composition of two symmetries (of an object or a physical theory) is again a symmetry. This gives a multiplication law on the symmetries which we call a group structure.

In this course you will learn to work with such group structures: we will start from finite groups to illustrate the basic definitions, but the main focus of this course lies on the Lie groups (continuous symmetries), especially for the unitary and rotation groups appearing in physics.

Apart from a few topological properties (compactness, connectedness, open and closed), we will also investigate the link between a Lie group and the associated Lie algebra (using the exponential map).

In a last part of the course, we will study 'representations' for Lie groups and algebras. Extra attention will obviously be paid to the spin representations for SU(2) and sl(2), and the representations for su(3) as these are related to quark models.

The course has an international dimension.

Class contact teachingLectures Practice sessions

ExaminationWritten with oral presentation Open-question

Course notes - available via Blackboard

"Introduction to group theory" Ledermann, Walter and Weir, Alan J., Harlow (1996)

david.eelbode@uantwerpen.be