**Lecturer:** F. Gelis

The QFT2 course is centered on two main pillars: path integral quantization and

functional methods, and non-abelian gauge theories. As a prerequisite, it assumes a good knowledge of basic quantum field theory (canonical quantization, perturbation theory, scalar field theory and basics of quantum electrodynamics).

The first part of this course will devoted to the path integral approach in quantum field theory. Starting with elementary examples in quantum mechanics, we will firstly revisit the theory of an interacting scalar field with functional methods. Then, we will discuss the case of fermionic fields and introduce Grassman variables. Focusing on quantum electrodynamics, we will use these functional techniques in order to derive the Schwinger-Dyson equations.

The part on non-abelian gauge fields will start with a discussion of non-abelian Lie groups and algebras, their representations and of the field structures that admit such a local symmetry. Then, we will proceed with the path integral quantization of a vector field with an SU(N) local gauge symmetry, following the Fadeev-Popov method. After having derived the Feynman rules, we will discuss the unitarity and renormalizability of such a field theory, focusing on the aspects that make them different from simpler theories such as QED. An important step for this will be the BRST symmetry. The course will finish with an introduction to lattice field theory.

**ECTS:** 4

- Teaching coordinator: François Gelis
- Teaching coordinator: Stéphane Munier
- Teaching coordinator: Pascal Paganini