Relativistic Quantum Mechanics

Wintersemester 2020/2021
Dozent: Weber
Link zum LSF
21 Teilnehmer/innen

General Remarks

A course in Relativistic Quantum Mechanics serves several purposes in the modern physics curriculum:

1. It provides a fast, intuitive, but not entirely strict, route to Feynman diagrams, which have become the language of Theoretical Particle Physics and are also employed in several other areas.

2. It can be used as an efficient preparation for a more formal Quantum Field Theory course, for which it provides many technical tools and important physical insights.

3. Many, if not all, of the ideas that have been developed in the course of the formulation of a relativistic version of Quantum Mechanics, are still relevant today, in one guise or the other, and sometimes quite surprisingly (for example, for the properties of graphene).

Lectures

After giving it quite some thought and taking into account the present situation as well as the peculiarities of the lecture hall (in the wintertime), I have arrived at the decision that the lectures will be entirely online, contrary to my original intention. Even though the online format is certainly not the natural nor the most efficient way of teaching, I think that, for now, we have to prioritize everybody’s health and safety.

Exercise sessions

There will be a two-hour exercise session every week. The schedule of the exercise sessions will be determined during the first lecture on Tuesday, November 3, with the participation of the students.

References

The principal reference for the course is the book "Relativistic Quantum Mechanics" by J.D. Bjorken and S.D. Drell, chapters 1 through 7 or 8. There are many other books that cover an important part of the topics of the course, for example,

W. Greiner, "Relativistic Quantum Mechanics",

F. Halzen and A.D. Martin, "Quarks and Gluons: An Introductory Course in Modern Particle Physics",

I.J.R. Aitchison and A.J.G. Hey, "Gauge Theories in Particle Physics: A Practical Introduction", Vol. I.

There is also a good chance that your favourite Quantum Mechanics book provides an introduction to Relativistic Quantum Mechanics. On the other hand, many books on Quantum Field Theory contain material on Relativistic Quantum Mechanics, in particular on the Dirac equation and on the evaluation of Feynman diagrams. Additional references for specific topics will be given during the course.

Although somewhat more advanced, Feynman's original articles are also very readable:

R.P. Feynman, "The Theory of Positrons", Phys. Rev. 76, 749 (1949),

R.P. Feynman, "Space-Time Approach to Quantum Electrodynamics", Phys. Rev. 76, 769 (1949).

Contents of the course

Here is the preliminary outline of the course (preliminary because it may suffer minor modifications during the actual lectures):

1. Klein-Gordon equation

Motivation; free-particle solutions; 4-current density; Feynman-Stueckelberg interpretation; minimal coupling to an electromagnetic field

Additional references

on the Feynman-Stueckelberg interpretation:

E.C.G. Stueckelberg, "Remarque à propos de la création de paires de particules en théorie de relativité", Helv. Phys. Acta 14, 588 (1941),

R.P. Feynman, "A Relativistic Cut-Off for Classical Electrodynamics", Phys. Rev. 74, 939 (1948),

F. Halzen and A.D. Martin, "Quarks and Gluons: An Introductory Course in Modern Particle Physics",

I.J.R. Aitchison and A.J.G. Hey, "Gauge Theories in Particle Physics: A Practical Introduction", Vol. I.

on the gauge principle:

I.J.R. Aitchison and A.J.G. Hey, "Gauge Theories in Particle Physics: A Practical Introduction", Vols. I and II.

2. Dirac equation

Dirac's historical derivation; 4-current density; nonrelativistic limit

3. Covariance of the Dirac equation

Manifestly covariant notation; spinor representation of the Lorentz group; parity transformation; bilinear covariants

4. Free-particle solutions

Lorentz transformation of the rest frame solutions; projection operators for energy and spin; problems with the physical interpretation; Foldy-Wouthuysen transformation

5. Hydrogen atom

Relativistic corrections; exact solution; discussion

6. Hole theory

Dirac sea and positrons; charge conjugation; time reversal

7. Propagator theory

Nonrelativistic propagator; scattering matrix; Feynman propagator for the Klein-Gordon equation; Feynman propagator for the Dirac equation

8. Simple scattering processes

Coulomb scattering of electrons, cross section, trace theorems; electron-muon, electron-electron and electron-positron scattering; Compton scattering; pair annihilation

9. Radiative corrections (time permitting)

Materialien

Übungsblätter

Exercises 1
- RQM_Exercises_1.pdf
Exercises 2
- RQM_Exercises_2.pdf
Exercises 3
- RQM_Exercises_3.pdf
Exercises 4
- RQM_Exercises_4.pdf
Exercises 5
- RQM_Exercises_5.pdf
Exercises 6
- RQM_Exercises_6_corrected.pdf
Exercises 7
- RQM_Exercises_7.pdf
Exercises 8
- RQM_Exercises_8.pdf
Exercises 9
- RQM_Exercises_9.pdf
Exercises 10
- RQM_Exercises_10.pdf
Exercises 11
- RQM_Exercises_11.pdf
Exercises 12
- RQM_Exercises_12.pdf

Übungsgruppen

Gruppe 01 (Gonzalo Alonso Alvarez)
21 Teilnehmer/innen
548-743-2267, Fr 11:15 - 13:00