"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: 7.5 Level: 2 Grading: A, B, C, D, E, Fx, F

Time: Period 3 (Lectures 36h, which will be given in English.)

Lecturer and examiner: Prof. Tommy Ohlsson
Telephone: 08-7908261 E-mail: see bottom of page

Aim

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. The Lorentz and Poincaré groups. Casimir
operators. Irreducible representations of particles. The Klein-Gordon
equation. The Dirac equation. The structure of Dirac particles. The
Dirac equation: central potentials. The Weyl equation.

II. Introduction to relativistic quantum field theory

Neutral and charged Klein-Gordon fields. The Dirac field. The Majorana
field. Maxwell's equations and quantization of the electromagnetic
field. Introduction to Yang-Mills theory. Asymptotic fields: LSZ
formulation. Perturbation theory. Introduction to quantum
electrodynamics. Interacting fields and Feynman diagrams. Elementary
processes of quantum electrodynamics. Introduction to regularization, renormalization, and radiative corrections.

Hand in assignments (INL1; 4.5 hp) and an oral exam (TEN1; 3 hp).

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 15 minutes. 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: A, B, C, D, E, Fx, and F. The grades will be awarded according to the following scheme:

Grade

Homework problems

Oral examination

F

< 40% of all problems correct

Failed

Fx

< 40% of all problems correct

Passed

Fx

≥ 40% of all problems correct

Failed

E

≥ 40% of all problems correct

Passed

D

≥ 60% of all problems correct

Passed

C

≥ 70% of all problems correct

Passed

B

≥ 80% of all problems correct

Passed

A

≥ 90% of all problems correct

Passed

In addition, you need to obtain at least 40 % on each homework problem set in order to obtain a passing grade (E or higher). If you obtain a total result of more than 40 %, but do not fulfill this criterion, you will be given the grade Fx and a chance to make a completing task for the grade E.
For PhD students, the different grades are: U (fail) and G (pass).

Required reading

The course literature consists of one book (mainly):

T. Ohlsson, Relativistic Quantum Physics - From Advanced Quantum Mechanics to Introductory Quantum Field Theory, Cambridge (2011)

Additional reading

Further recommended reading:

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

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

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

F. Mandl and G. Shaw, Quantum Field Theory, rev. ed., Wiley (1994)

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

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

F. Schwabl, Advanced Quantum Mechanics, Springer (1999)

S.S. Schweber, An Introduction to Relativistic Quantum Field Theory, Dover (2005)

F.J. Ynduráin, Relativistic Quantum Mechanics and Introduction to Field Theory, Springer (1996)