# Quantum field theory II

## Summary

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.

## Content

**8. Quantized Electromagnetic field**. Gauge Invariance. Gauss Law and physical degrees of freedom. Quantization in the Coulomb and Lorenz gauges.

**9. Massive vector field**. Non-linearly realized gauge symmetry. Higgs mechanism. Quantized massive vector field. The action of the Lorentz group on the spin polarization.

**10. Discrete symmetries**: P, C, T and CPT.

**11. Causality** with classical and with quantum fields.

**12. Interacting fields**. Formal theory of relativistic scattering. Asymptotic states. Lippmann-Schwinger equation. The S-matrix and its symmetries. The S-matrix in perturbation theory: Wick theorem and Feynman diagrams. Cross sections and decay-rates.

**13.** **Quantum electrodynamics**. Feynman rules and fundamental processes (Compton scattering, electron positron annihilation). Ward identities and gauge invariance.

**14. Non-Abelian gauge theories and the Standard Model. **Gauge group structure and field content of the Standard Model**. **Electroweak unification and the Higgs mechanism. Low energy phenomenology of electroweak interactions. Parity violation. Precision electroweak tests and the Higgs boson.

## Learning Prerequisites

## Required courses

Classical Electrodynamics, Quantum Mechanics I and II, Analytical Mechanics, Mathematical Physics

## Recommended courses

Quantum Mechanics III and IV, General Relativity, Cosmology

## Learning Outcomes

By the end of the course, the student must be able to:

- Expound the theory and its phenomenological consequences
- Formalize and solve the problems

## Transversal skills

- Use a work methodology appropriate to the task.

## Teaching methods

Ex cathedra and exercises in class

## Assessment methods

Exam: oral, consisting of one theoretical question and one exercise, picked randomly and for which the candidate is allowed a 60 minute preparation

## Resources

## Bibliography

- "An introduction to quantum field theory / Michael E. Peskin, Daniel V. Schroeder". Année:1995. ISBN:0-201-50397-2
- "The quantum theory of fields / Steven Weinberg". Année:2005. ISBN:978-0-521-67053-1
- "Quantum field theory / Claude Itzykson, Jean-Bernard Zuber". Année:1980. ISBN:0-07-032071-3
- "Relativistic quantum mechanics / James D. Bjorken, Sidney D. Drell". Année:1964
- "A modern introduction to quantum field theory / Michele Maggiore". Année:2010. ISBN:978-0-19-852074-0
- "Théorie quantique des champs / Jean-Pierre Derendinger". Année:2001. ISBN:2-88074-491-1

## Ressources en bibliothèque

- An Introduction to Quantum Field Theory / Peskin
- The Quantum Theory of Fields/ Weinberg
- Quantum Field Theory / Itzykson
- A Modern Introduction to Quantum Field Theory / Maggiore
- Théorie quantique des champs / Derendinger
- Relativistic Quantum Mechanics / Drell

## Websites

## Moodle Link

## Prerequisite for

Prerequisite for Theoretical Physics

## In the programs

**Semester:**Spring**Exam form:**Oral (summer session)**Subject examined:**Quantum field theory II**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Oral (summer session)**Subject examined:**Quantum field theory II**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Oral (summer session)**Subject examined:**Quantum field theory II**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Oral (summer session)**Subject examined:**Quantum field theory II**Lecture:**3 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks