Mathematical methods in physics: geometry and group theory 1

A.Y. 2016/2017
6
Max ECTS
48
Overall hours
SSD
FIS/02
Language
Italian
Learning objectives
Lo studente deve arrivare a comprendere e sapere maneggiare i Gruppi di Lie, le Algebre di Lie e le loro rappresentazioni.
Expected learning outcomes
Undefined
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
- Differential geometry: manifolds, tangent and cotangent spaces and bundles, vector fields, differential forms.
- Lie groups and Lie algebras. Relation between algebra and group. One parameter subgroups. Exponential map. Adjoint representation. Killing form.
- The classification of complex semisimple Lie algebras: Cartan
subalgebras, roots, Dynkin diagrams. Real forms.
- Irreducible representations of semisimple Lie algebras. Relations
between representations of a Lie algebra and of the associated Lie group. Weights. Products of representations.
- Subalgebras and subgroups. Branching rule of representations.
- Analysis of symmetries with particular relevance in physics. The unitary groups SU(n). The Poincare' group, classification of its representations by means of mass and spin.
- Homogeneous spaces.
- Clifford algebras.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 6
Lessons: 48 hours
Professor(s)