# 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

This introductory course stresses the importance that quantum fields play in the description of relativistic particles, and vice versa.

The course starts with a quantum-field theoretical description of particles of spin-0, described by scalar fields; it focusses on:

- The notion of relativistic scalar field, introduced as a trivial representations of the Lorentz group

- Field dynamics, discussed first in classical field theory (e.g Noether theorem, action principle and Euler-Lagrange equations)

- Field quantization: Fock space, the existence of anti-particles, causality

- Perturbation theory, S-matrix, LSZ formalism, Feynman diagrams

- Applications to the computation of scattering and decay processes

- Introduction to Renormalization theory

Depending on time, the course will include other topics relevant for the description of spin-0 particles (e.g. Goldstone theorem and effective field theories)

## Learning Prerequisites

## Required courses

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

## Recommended courses

General Relativity and Quantum Mechanics III warmly recommended.

## 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

2 hours of the course will be given online (zoom)

1 hour course + exercices will be on site

## Assessment methods

Oral, consisting of one theoretical question and one exercise, picked randomly and for which the candidate is allowed a 30 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

## Ressources en bibliothèque

- An Introduction to Quantum Field Theory / Peskin
- The Quantum Theory of Fields / Weinberg
- A Modern Introduction to Quantum Field Theory / Maggiore
- Relativistic Quantum Mechanics / Drell
- 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