Advanced Quantum Field Theory
PHYS-702 / 4 credits
Teacher(s): Bellazzini Brando, Invited lecturers (see below), Rattazzi Riccardo
Language: English
Remark: Next time: Fall 2023
Frequency
Every year
Summary
The course builds on the course QFT1 and QFT2 and develops in parallel to the course on Gauge Theories and the SM.
Content
The course is essentially divided into two parts. The first smaller part is a revisitation of the notions of field and particle in QFT, starting from fundamental principles of symmetry and locality. The central result is the classification of single particle and multiparticle states according to the unitary representations of the Poincaré group. The second and main part concerns the study of quantum effects. In perturbation theory, these are associated to Feynman diagrams with loops. The concepts of ultraviolet divergence and renormalization are introduced. Non-abelian gauge theories are also discussed. Skills developed in the course include the use of the Path integral formalism, methodologies to perform loop calculations and renormalization. Applications to particle physics are also illustrated.
1) Brief foray into axiomatic QFT
- Unitary representations of the Poincaré group
- Fields and the cluster property
- LSZ formula for the S-matrix
2) Path Integral approach to QFT
- Quantization of non-abelian gauge theories
3) Regularization and Renormalization
- Applications to QFTs with scalars, fermions and Abelian gauge fields, in particular to Quantum Electrodynamics
- Effective action and Effective Potential
5) The renormalization group
- asymptotic freedom and fixed points
Keywords
Path integral formalism, divergences renormalization, Gauge theories
Renormalization group, Anomalies
Learning Prerequisites
Required courses
Quantum mechanics 1,2 - Quantum Field theory 1,2
Recommended courses
Conformal Field theory and gravity
Gauge theories and the Standard Model
Learning Outcomes
By the end of the course, the student must be able to:
- Study a quantum field theory at quantum level
- Understanding and interpreting loop effects in a quantum field theory
- Performing loop calculations in gauge theories
Resources
Bibliography
An introduction to Quantum Field Theory, by Peskin and Schroeder
The quantum theory of Fields, Vol 1,2 by Weinberg
Ressources en bibliothèque
- An introduction to Quantum Field Theory / Peskin, Schroeder
- The quantum theory of fields / Weinberg . Vol2
- The quantum theory of fields / Weinberg . Vol1
Moodle Link
In the programs
- Exam form: Multiple (session free)
- Subject examined: Advanced Quantum Field Theory
- Lecture: 42 Hour(s)
- Exercises: 14 Hour(s)
- Type: optional