# Quantum field theory I

## Summary

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

## Content

**1. Introduction. **Fundamental motivations for quantum field theory, Natural units of measure, Overview of the Standard Model of particle physics.

**2. Classical Field Theory.** Lagrangian and Hamiltonian formulation.

**3. Symmetry Principles.** Elements of group theory, Lie groups, Lie Algebras, group representations, Lorentz and Poincaré groups.

**4. Symmetries and Conservation laws. **Noether Theorem. Conserved currents and conserved charges. The conserved charges of the Poincarè group and their interpretation.

**4. Canonical quantization** of real and complex scalar fields. Creation and annihilation operators. Fock space. Bose-Einstein statistics. Heisenberg picture field. Realization of symmetries in the quantum theory.

**5. Spinorial representations** of the Lorentz group. Weyl, Majorana and Dirac spinors and their wave equations. Quantization of the Dirac field. Anticommutation relations and Fermi-Dirac statistics.

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

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

## Learning Prerequisites

## Required courses

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

## Recommended courses

General Relativity warmly recommmended

## 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
- Théorie quantique des champs / Derendinger
- Relativistic Quantum Mechanics / Drell
- A Modern Introduction to Quantum Field Theory / Maggiore
- Quantum Field Theory / Itzykson

## Websites

## Moodle Link

## Prerequisite for

Recommended for Theoretical Physics and for Particle Physics

## In the programs

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

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

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

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