Description

This course provides an introduction to relativistic quantum mechanics, which unifies the principles of quantum mechanics and relativity. Unlike in non-relativistic quantum mechanics, the relativistic counterpart of the Schrödinger equation depends on the spin of the particle it describes. Two fundamental relativistic equations will be studied: the Klein–Gordon equation for spinless particles and the Dirac equation for spin-1/2 fermions.

The aim of these lectures is to study the Klein–Gordon and Dirac equations and to provide the necessary tools for analyzing relativistic corrections in quantum physics. These lectures form an essential foundation for the study of second quantization, that is, quantum field theory —the cornerstone of the Standard Model of particle physics.

Compétences visées

•    Applying knowledge in physics;

•    Apply methods from mathematics and digital technology;

•    Produce a critical analysis, with hindsight and perspective;

•    Interact with colleagues in physics and other disciplines;

•    Research a physics topic using specialised resources;

•    Communicate in writing and orally, including in English;

•    Respect ethical, professional and environmental principles in the practice of physics.

Syllabus

1) From Quantum physics to Relativistic Quantum Physics
  1.1) Brief summary of quantum and relativistic physics 
  1.2) Relativistic quantum mechanics: description of a spin-s particle
  1.3) The problem of negative energy particle
  1.4) Lagrangian formalism in field theory
  
2) Spin zero-particles: the Klein-Gordon equation
  2.1) Plane wave solutions
  2.2) Lagrangian of the Klein-Gordon equation
  2.3) Coupling to electromagnetism
  2.4) First order formalism
  2.5) Discrete symmetries
  2.6) Negative energy solutions 
  2.7) One particle interpretation of Klein-Gordon equation
  2.8) Klein paradox
  
3) Spin 1/2-particles: the Dirac equation
   3.1) Dirac gamma-matrices and Dirac spinors
   3.2) Spin content of the Dirac equation
   3.3) Chiral representation and Weyl spinors
   3.4) Discrete symmetries
   3.5) Lagrangian of Dirac equation
   3.6) Solutions of Dirac equation
   3.7) Helicity and chirality
   3.8) Coupling to electromagnetism
   3.9) Klein paradox
   3.10) Non relativistic limits and gyromagnetic ratio

Bibliographie

1. A. Wachter,  Relativistic quantum mechanics, Theoretical and Mathematical Physics, Springer, New York, 2011.
2. P. Strange,  Relativistic Quantum Mechanics: With Applications in Condensed Matter and Atomic Physics, Cambridge University Press; 1998.
3.  I. J. R. Aitchison and A. J. G. Hey, Gauge Theories in Particle Physics: A Practical Introduction  (Fourth Edition) 2013, Taylor & Francis
4.  F. Gross, Relativistic quantum mechanics and field theory, reprint of 1993 original, A Wiley-Interscience Publication Wiley Science Paperback Series, , Wiley, New York, 1999.

Contacts

Responsable pédagogique

• Michel Rausch De Traubenberg

MCC

Les épreuves indiquées respectent et appliquent le règlement de votre formation, disponible dans l'onglet Documents de la description de la formation.

Régime d'évaluation

CT (Contrôle terminal, mêlé de contrôle continu)

Coefficient

1.0

Évaluation initiale / Session principale - Épreuves

Seconde chance / Session de rattrapage - Épreuves