"Relativistic Quantum Physics" is a course where important theories
for elementary particle physics and symmetries are learned. During the
course, it will be illustrated how relativistic symmetries and gauge
symmetries can restrict "possible" theories. The course will give an
introduction to perturbation theory and Feynman diagrams. The problem
with divergencies will be mentioned and the concepts for
regularization and renormalization will be illustrated.

Credits: 5 ECTS Credits: 7.5 Level: D Grading: U, 3, 4, 5

Time: Period 2, 3 (Lectures 30h, which will be given in English.)

After completion of the course you should be able to:

apply the Poincaré group as well as classify particle representations.

analyze the Klein-Gordon and the Dirac equations.

solve the Weyl equation.

know Maxwell's equations and classical Yang-Mills theory.

quantize Klein-Gordon, Dirac, and Majorana fields as well as formulate the Lagrangian for these fields.

use perturbation theory in simple quantum field theories.

formulate the Lagrangian for quantum electrodynamics as well as analyze this.

derive Feynman rules from simple quantum field theories as well as interpret Feynman diagrams.

analyze elementary processes in quantum electrodynamics.

compute radiative corrections to elementary processes in quantum electrodynamics.

Syllabus

I. Relativistic quantum mechanics

Tensor notation. Casimir operators. The Poincaré group. Irreducible
representations of particles. The Klein-Gordon equation. The Dirac
equation. The structure of Dirac particles. The Dirac equation:
central potentials. The Weyl equation. Maxwell's equations and
quantization of the electromagnetic field. Introduction to Yang-Mills
theory.

II. Introduction to quantum field theory

Neutral and charged Klein-Gordon fields. The Dirac field. The Majorana
field. Asymptotic fields: LSZ formulation. Perturbation
theory. Introduction to quantum electrodynamics. Interacting fields
and Feynman diagrams. Elementary processes of quantum
electrodynamics. Introduction to radiative corrections.

Hand in assignments (INL1; 3 p) and an oral exam (TEN1; 2 p).

Examination

The examination of the course will be a combination of homework problems and an oral examination. There will be three sets of homework problems during the course. These will be distributed and should be handed in according to the following scheme:

The oral examinations will take place after the last lecture of the course. Each examination will take approximately one hour. The time for the examination will be agreed upon between the student and the examiner, but the student is obliged to take contact with the examiner.

Grading

The different grades are: U, 3, 4, and 5. The grades will be awarded according to the following scheme:

Grade

Homework problems

Oral examination

U

< 40% of all problems correct

Failed

< 40% of all problems correct

Passed

≥ 40% of all problems correct

Failed

3

≥ 40% of all problems correct

Passed

4

≥ 60% of all problems correct

Passed

5

≥ 80% of all problems correct

Passed

For PhD students, the different grades are: U (fail) and G (pass). Here the grade G corresponds to the grade 5 for the undergraduate students, whereas the grade U corresponds to the grades U, 3, and 4 for the undergraduate students.

Required reading

The course literature consists of two books (mainly):

A.Z. Capri, Relativistic Quantum Mechanics and Introduction to Quantum Field Theory, World Scientific (2002)

M.E. Peskin and D.V. Schroeder, Introduction to Quantum Field Theory, Harper-Collins (1995)

Additional reading

Further recommended reading:

C. Doran and A. Lasenby, Geometric Algebra for Physicists, Cambridge (2003)

W. Greiner, Relativistic Quantum Mechanics - Wave Equations, Springer (2000)

F. Gross, Relativistic Quantum Mechanics and Field Theory, Wiley (1993)

J. Mickelsson, T. Ohlsson, and H. Snellman, Relativity Theory, KTH (2005)