Description

Group theory is an important tool for gaining a deeper understanding of the laws of physics. For example, the spectrum of a Hamiltonian in quantum mechanics can be organised using group theory. In particle physics —which is both a quantum and relativistic theory— group theory plays an even more significant rôle, as it describes how elementary particles behave and interact with one another.

The aim of these lectures is to provide an introduction to Lie groups from a practical perspective.  The various concepts will be introduced gradually. Several direct applications will be presented throughout. These lectures will be particularly useful in contexts where the concept of symmetry plays a central rôle. The techniques introduced here can be extended to theories based on symmetry principles, such as the Standard Model of particle physics, supersymmetry, grand unified theories, etc.

Although focused on continuous groups or Lie groups, this course will also allow for an understanding of systems with discrete symmetry groups, such as those found in crystallography or condensed matter physics.

Compétences visées

•    Applying knowledge in physics;

•    Apply methods from mathematics and digital technology;

•    Produce a critical analysis, with hindsight and perspective;

•    Communicate in writing and orally, including in English.

Syllabus

1) Generality
2) Three dimensional Lie groups
3) The Lie group SU(3)
4) Orthogonal and Unitary Lie groups
5) Simple Lie groups
6) Finite groups

Bibliographie

 R.~Campoamor-Stursberg et M.~Rausch de Traubenberg, Group Theory in Physics A Practitioner's Guide, https://www.worldscientific.com/worldscibooks/10.1142/11081 World Scientific (2018) 760 pages, ISBN: 978-981-3273-60-3 DOI:10.1142/11081

Contacts

Responsable(s) de l'enseignement

• Michel Rausch De Traubenberg

MCC

Les épreuves indiquées respectent et appliquent le règlement de votre formation, disponible dans l'onglet Documents de la description de la formation.

Régime d'évaluation

CT (Contrôle terminal, mêlé de contrôle continu)

Coefficient

1.0

Évaluation initiale / Session principale - Épreuves

Seconde chance / Session de rattrapage - Épreuves