The course will take place in the second half of the fall semester 2019 (03.12 - 19.12) on Tuesdays (10:15 - 13:00) and Thursdays (10:00 - 12:00) in room B1.
Course description
The purpose of these 6 lectures is to expose the modern techniques to build concretely the perturbative quantum field theory of the Yang-Mills action coupled to matter, with or without spontaneous symmetry breaking, as well as to explain the underlying geometry of the process.
A main ingredient is the systematic use of the BRST symmetry, the quantum generalisation of the classical Yang-Mills symmetry.
The lecture will cover with many details:
- A reminder of the functional methods to formulate in the most efficient way the perturbative renormalisation program in the presence of local symmetries
- The gauge-fixing process of the path integral of the Yang-Mills quantum theory and the role of the BRST symmetry
- The construction of the BRST symmetry both in a down to earth way and in a geometrical way
- The proof of the renormalisability of the theory
- The Yang-Mills quantum anomalies and their cancellation conditions
- The role of the Batali-Vilkowiski antifields and their roles in the renormalisation of the theory
These questions will be treated in view of mastering in a safe way all computations needed to compare the predictions of the theory to the experimental data.
Besides, the beautiful geometrical context that illuminates all these technical properties will be explained
If there is time left, the methodology used to quantise the Yang-Mills action will be generalised to other theories, where analogous quantum geometrical patterns also arise
Lecturer
Prof. L. Baulieu
