PHY2125 : Mécanique Quantique Relativiste



Introduction

A complement to the Quantum Mechanics courses (I and II) and propedeutic to Quantum Field Theory (I and II). It presents the implications of imposing Lorentz invariance to quantum mechanics. This course is 15h (lectures) + 15h (tutorials) and it is worth 4 credits. Lectures are given in English or French.

Lecturers

Lectures: Prof. Fabio Maltoni
Center for Particle Physics and Phenomenology - CP3
Tel: 01047 3166
Room: e.353
E-mail: maltoni_AT_fyma.ucl.ac.be

Tutorials: Dr. Keith Hamilton
Center for Particle Physics and Phenomenology - CP3
Tel: 01047 3239
Room: e.255
E-mail: Keith.Hamilton_AT_uclouvain.be

Timetable and location

Lectures are given for 14 weeks starting

  • Tuesday - from 16:15 to 17:45 in CYCL04

Program

  • Historical introduction
  • Review of QM and Special Relativity
  • Klein-Gordon equation
    • probability density and current : problems and interpretation
    • Free solutions
    • Non-relativistic limit
    • The Schroedinger form of the K-G Equation
    • Charge conjugation
  • Dirac equation
    • Linearization and gamma's technology
    • Lorentz covariance
    • Non-relativistic limit
    • Spinors
  • Dirac particles in external fields
    • Central potential and the angular momentum
    • Hydrogen Atom
    • EM field: electric and dipole moments
  • Discrete symmetries: C, P, and T
  • Neutrinos : Dirac vs. Majorana

References

Hereafter, I only mention a few books, which might be used as references and/or for exercises:

  • W. Greiner, Relativistic Quantum Mechanics, Springer-Verlag , [Grei]
  • J. J . Sakurai, Advanced Quantum Mechanics, ed. Addison-Wesley, [Saku]
  • Steven Weinberg, Quantum Field Theory, vol I, ed. Cambridge, [Wei]

Exercises

Exercises by K. Hamilton that will be discussed during the tutorials can be found here.

Projects

Here are a few proposals for final projects

  • SUSY: Study and present the first three chapters of hep-ph/0505105
  • Majorana's Neutrinos : See-saw mechanism, neutrino oscillations, EM properties, Double-beta decay. ( hep-ph/0410370 , Mohapatra's book on "Massive neutrinos").

Syllabus

Week

Dates

Lectures & Tutorials

Notes

 

1

 

Tue 16 Sep


I Lecture:
Historical Introduction and presentation of the course


Chapter I [Wei]

 

2

 

Tue 23 Sep


II Lecture :
Review of Symmetries in Classical Mechanics and quantum Mechanics. Wigner's Theorem. Special Relativity. Lorentz and Poincare' groups. Maxwell Equations.



Notes by J. Govaerts on PHY1223
Chapter II [Wei] , Chapter I [Grei]

 

3

 

Tue 30 Sep


Tutorial : Homework discussion and Exercises



 

4

 

Tue 7


IV Lecture :
The Klein-Gordon equation



Chapter I [Grei]

 

5

 

Tue 14 Oct


V Lecture :
The Dirac equation


Chapter II [Grei]

 

6

 

Tue 21 Oct


Tutorial : Homework discussion and Exercises



 

7

 

Tue 28 Oct


VI Lecture :
The covariant form of the Dirac Equation



 

8

 

Tue 4 Nov


Tutorial : Exercises



 

9

 

Tue 11 Nov


Holidays



 

10

 

Tue 18 Nov


VIII Lecture :
Discrete symmetries



 

11

 

Tue 25 Nov


IX Lecture : Applications



 

13

 

Tue 2 Dec


X Lecture :
The high energy limit of the Dirac Equation. Chirality and neutrinos.



 

13

 

Tue 9 Dec


Tutorial : Exercises



 

14

 

Tue 16 Dec


XI Lecture :
Dirac vs Majorana neutrinos.