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Advanced Math. for Physics

These lectures allow to acquire familiarity and operational knowledge of the mathematics of symmetry groups, as a transversal and structuring notion of modern Physics, from condensed matter to particle physics.

Syllabus : " Advanced Mathematics for Physics "

- Lectures 20 hours, Tutorials 10 hours (2nd Semester) -

(Robin Zegers)

Chapter 1: General Group theory (definitions and main theorems)

Chapter 2: Finite and discrete groups
Examples include reflection groups and lattices in relation with crystallography, molecular physics etc. This chapter also introduces the notion of root systems as relevant to general Lie theory.

Chapter 3: Introduction to Lie groups and Lie algebras

Chapter 4: Introduction to the representation theory of Lie algebras
Special emphasis will be put on the Lie groups relevant to High Energy Physics such as the Poincaré and Lorentz groups; SU(2) and SU(3) in relation with particle physics.

Recommended textbooks:

  • Fulton and Harris, Representation Theory
  • Gilmore, Lie groups, Lie algebras and some of their applications
  • Georgi, Lie algebras in particle Physics
  • Hamermesh, Group theory and its applications to physical problems
  • Kosmann-Schwartzbach, Groups and symmetries
  • Sternberg, Group theory and physics

Course prerequisites and corequisites

- Elementary quantum mechanics (Hilbert spaces, operators);
- Elementary linear algebra (Vector spaces, matrices etc).

Course concrete goals

On completion of the course students should be able to:

— Handle the physically relevant mathematics of group theory and representation theory
— Manipulate the classical Lie groups and their representations
— Follow any advanced M2 lecture involving or relying on those notions.