SI2390 Relativistic Quantum Physics

SI2390 Relativistic Quantum Physics

"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: D     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: 08-55378161     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.

Prerequisites

The following courses are mandatory:
• Quantum Physics
• Special Relativity Theory
The following course is recommended:
• Classical Theoretical Physics

Requirements

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:
 Homework problems Out In Set #1 Lecture 5 (February 1, 2012) February 17, 2012 Set #2 Lecture 11 (February 16, 2012) March 7, 2012 Set #3 Lecture 17 (March 7, 2012) March 23, 2012
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.

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
For PhD students, the different grades are: U (fail) and G (pass).

The course literature consists of one book (mainly):
• T. Ohlsson, Relativistic Quantum Physics - From Advanced Quantum Mechanics to Introductory Quantum Field Theory, Cambridge (2011)