Quantum field theory

This course is an introduction to the quantum theory of relativistic fields and its applications in particle physics. Using the example of a scalar field, the formalisms of canonical quantization and path integral quantization will be developed before introducing perturbation theory and some notions of renormalization. We will discuss the quantization of spin 1/2 and spin 1 fields and end with a discussion of quantum electrodynamics.

Know the notions of a classical and quantized relativistic field and the formalisms of canonical and path integral quantization. Understand the necessity and some elementary techniques of renormalization, in particular dimensional regularization. Know how to calculate cross sections and decay rates at the level of one-loop diagrams in scalar theory and quantum electrodynamics.

Knowledge of physics, mathematics and English at the level of the bachelor's degree in physics and the M1 Cosmos, fields and particles. In particular special relativity, advanced quantum mechanics, electrodynamics, phenomenology of elementary particles.

Recommended Prerequisites:

Knowledge of functional analysis and complex analysis.

Final examination

Classic fields

Canonical quantization and path integral quantization

Perturbation theory, Feynman diagrams

Notions of renormalization

Fermionic fields, gauge fields and their quantization

Quantum electrodynamics at the level of tree and loop diagrams.