Description

Theoretical aspects of particle physics

Introduction and historical development

Part 1: Symmetry in Particle Physics
A first introduction to symmetries in Particle Physics, with an emphasis on their mathematical formulation. A key result is that the possible fields can be understood as the (irreducible) representations of the Lorentz group.
• Mathematical toolkit: Lie group, Lie algebra and linear representation
• Internal symmetries: U(n) and SU(n) groups
• Space-time symmetries: Poincaré and Lorentz groups
• Field classification according to Lorentz group representations

Part 2: Deriving Feynman rules from the Lagrangian density
This section is built on Michel Rausch de Traubenberg’s Quantum Field Theory (QFT) lectures, extending the treatment from scalar fields to spinor and vector fields. Each new topic will begin with a brief review of the relevant QFT concepts before moving on to their generalization.
• Classical theory of free fields (real scalar, complex scalar, spinor and vector)
• Canonical quantization of free fields
• Field interactions
• Scattering cross-sections and decay widths

Part 3: Building the Standard Model
We will construct consistent theories using Noether’s procedure. In particular, we will show how the interactions among fundamental particles emerge as a consequence of gauge symmetry invariance.
• Abelian gauge symmetry: Quantum Electrodynamics (QED)
• Non-abelian gauge symmetry: Yang-Mills theory and Glashow-Salam-Weinberg (GSW) electroweak theory
• Spontaneous symmetry breaking and the origin of mass in the Standard Model
• Tricks for calculating scattering cross-sections and decay widths

Autres contacts

Enseignant: Éric Conte <eric.conte@iphc.cnrs.fr>