This lecture aims to present the mathematics of quantum mechanics and more generally of quantum physics. It is mainly addressed to physicists or to mathematicians interested in the domain.
Presentation of Wightman's axiomatic framework to QFT as well as to the necessary mathematical objects to their understanding (Hilbert analysis, distributions, group representations,...).
Proofs of the main mathematical consequences (CPT, spin-statistics, Reeh-Schlieder, Haag no-go).
This first semester class is an introduction to the basis of differential calculus.
Presentation of standard fonction in analysis. Introduction to complex numbers and to polynomials. Developments of functions in Taylor series. Introduction to linear and ordinary differential equations of first and second order.
We present the fundamental notions of linear algebra in the geometric context where they emerged. We will therefore emphasize the dimensions 2 and 3, and insist on the visualisation of classical objects and operations in the plane and in the 3D space.
Read in french (requirement for this course).