Quantum field theory III
Summary
The course builds on QFT1-2 and develops in parallel to The Standard Model course. After briefly revisiting the notions of particle, field and S-matrix, the course fully develops the theory of Renormalization and closes on the quantization of non-abelian gauge theories.
Content
1) Brief foray into "axiomatic" QFT
-Unitary representations of the Poincaré group
- Fields, relativistic wave equations
- Cluster property and LSZ formula for the S-matrix
2) Path Integral approach to QFT
- Functional methods, Effective action
- Equations of motion, Ward identities, Goldstone theorem
3) Renormalization
- loop corrections and regularization methods
- renormalization with examples of its systematics
- applications to QFTs with scalars, fermions and Abelian gauge fields, in particular to Quantum Electrodynamics
4) The renormalization group
- asymptotic freedom and fixed points
- Callan-Symanzik equation
- renormalization of composite operators
5) Quantization of non-abelian gauge theories
- path Integral in gauge theories and Faddeev-Popov method
- ghosts and BRST symmetry
- physical states and unitarity
- Slavnov-Taylor identities and basics of renormalization
5) Infrared divergences (time permitting)
- soft photons and soft gravitons
- Lorentz invariance and current conservation (Weinberg)
- real and virtual emission of soft photons, cancellation of IR divergences
Keywords
Quantum Fields, LSZ Reduction, Renormalization, Renormalization Group, Composite Operators, Fixed Points, Gauge Theories, BRS symmetry
Learning Prerequisites
Required courses
QFT1, QFT2, QM3, QM4
Recommended courses
General Relativity and Cosmology 1
Learning Outcomes
By the end of the course, the student must be able to:
- Formulate
- Analyze
- Reason
- Model
- Solve
- Illustrate
- Compute
- Demonstrate
Transversal skills
- Use a work methodology appropriate to the task.
Teaching methods
A mix of inverted class, based on recorded lectures from previous years, and of ex cathedra lectures
Expected student activities
Weekly take home exercises, with weekly assessment
Assessment methods
Weekly exercises during the semester: 20% of evaluation
Take home written exam: 30% of evaluation
Oral exam: 50% of evaluation
Resources
Bibliography
- The Quantum Theory of Fields I and II, Steve Weinberg
- An Introduction to Quantum Field Theory, Peskin-Schroeder
Ressources en bibliothèque
Notes/Handbook
Handwritten Notes
Moodle Link
Dans les plans d'études
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Quantum field theory III
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Quantum field theory III
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Quantum field theory III
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Semestre: Automne
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Quantum field theory III
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: optionnel
- Forme de l'examen: Oral (session d'hiver)
- Matière examinée: Quantum field theory III
- Cours: 3 Heure(s) hebdo x 14 semaines
- Exercices: 1 Heure(s) hebdo x 14 semaines
- Type: obligatoire