Introduction to
Quantum Field Theory
FYTN10, 7.5 hp
Spring 2013

The official home page for the course is at http://www.thep.lu.se/english/education/courses/introduction_to_quantum_field_theory

This homepage was for the 2013 course.

You can find the homepage of the 2014 course here

General Information

This is a 7.5 hp course on Quantum Field Theory. It is an introductory course covering essentially the first six chapters of the book by Peskin and Schroeder (see below). The course is scheduled for the first part of the semester (January 21 to March 24).

Description

This course introduces the theoretical concepts, based on quantum mechanics and the special theory of relativity, needed to describe relativistic particles and their interactions. The course starts out with the Klein-Gordon and Dirac field equations, describing free scalar particles and fermions respectively, and their quantization. It is then shown how interactions can be included in perturbation theory and how they can be described through Feynman diagrams. These techniques are then applied mainly to calculate tree-level processes in quantum electrodynamics. The course ends with a short introduction to higher order processes and radiative corrections.

Prerequisites

Quantum mechanics (especially time-dependent perturbation theory) at a level corresponding to FYTA12 (fundamental theoretical physics) or FYSN17 (quantum mechanics) as well as more in-depth knowledge corresponding to at least one of the courses FYTN04 (theoretical particle physics) or FYST37 (modern quantum mechanics). In addition FYTN01 (mathematical methods of physics) is recommended.

Format

The course will consist of approximately 20 lectures (2x45min) and 4-5 problem solving sessions.

Preliminary schedule

The course will start on January 21 and then continue with 2-4 sessions per week until March 22. The introductory meeting will be 13-15 on January 21 and then the lectures will be as follows with tentative subjects

Date	Time	Place	Subject	Peskin and Schroeder	Hand-in exercise
Mon 21/1	13-15	Sal NB	Introduction
Wed 23/1	10-12	Sal NB	Classical field theory, Noether's theorem	Chapter 2.1-2.2
Fri 25/1	13-15	Sal NB	Klein-Gordon field, causality and progator	Chapter 2.3-2.4 (7.1)
Mon 28/1	13-15	Sal NB	Perturbation theory and Correlation fcn's	Chapter 4.1-4.2
Wed 30/1	10-12	Sal NB	Problems chapter 2	-	nr 1
Fri 1/2	13-15	Sal NB	Wick's theorem, Feynman diagrams	Chapter 4.3-4.4
Mon 4/2	13-15	Sal NB	Cross-sections	Chapter 4.5
Wed 6/2	10-12	Sal NB	S-matrix from Feynman diagrams	Chapter 4.6 (7.2)
Fri 8/2	13-15	Sal NB	Dirac field, Weyl representation	Chapter 3.1-3.2	nr 1 due
Mon 11/2	13-15	Sal NB	Free particle solutions, Dirac bilinears	Chapter 3.3-3.4
Thu 14/2	10-12	Sal NB	Problems chapter 4.1-4.6	-	nr 2
Fri 15/2	13-15	Sal NB	Quantization of Dirac Field	Chapter 3.5
Mon 18/2	13-15	Sal NB	Discrete symmetries of Dirac Field	Chapter 3.6
Wed 20/2	10-12	Sal NB	Feynman rules for fermions	Chapter 4.7	nr 2 due
Fri 22/2	13-15	Sal NB	Yukawa theory and QED	Chapter 4.8
Mon 25/2	13-15	Sal NB	e+e- -> mu+mu-: introduction	Chapter 5.1
Wed 27/2	10-12	Sal NB	Problems chapter 3 and 4.7-4.8	-	nr 3
Fri 1/3	13-15	Sal HUB	e+e- -> mu+mu-: helicity structure	Chapter 5.2
Mon 4/3	13-15	Sal NB	Non-relativistic limit, Crossing symmetry	Chapter 5.3-5.4
Wed 6/3	10-12	Sal NB	Compton scattering	Chapter 5.5	nr 3 due
Fri 8/3	13-15	Sal NB	Bremsstrahlung and electron vertex correction	Chapter 6.1-6.2
Mon 11/3	13-15	Sal NB	Problems chapter 5	-	nr 4
Wed 13/3	10-12	Sal NB	Electron vertex correction: UV and infrared divergences	Chapter 6.3-6.4
Fri 15/3	13-15	Sal NB	Summation and interpretation of infrared divergences	Chapter 6.5
Mon 18/3	10-12	Sal NB	Renormalisation and outlook	Chapter 7	nr 4 due
Wed 20/3	10-12	Sal NB	Question and Answer session
Thu 21/3	-	-	Oral exams
Fri 22/3	-	-	Oral exams

Problems

Download problems for chapter 2 here
Download problems for chapter 4.1-4.6 here
Download problems for chapter 3 and 4.7-4.8 here
Download problems for chapter 5 here

Examination

The examination will be in the form of hand-in exercises, active participation in problem solving sessions and an oral examination at the end of the course.

Oral exam

The starting point for the oral exam is your solutions to the hand-in exercises. In addition it is assumed that you have done and understood all the problems for the problem solving sessions. Finally, regarding the higher order corrections you should have an overall understanding of the origin of real and virtual corrections, why they are divergent, and how these divergencies are dealt with both technically and physically. You can find some examples of questions on radiative corrections here. I have also to put together a more general list of questions that indicate the level I expect for the oral exam.

Note: You have to have completed all hand-in exercises successfully before the oral exam.

Course evaluation

To help us improve our courses we want you to complete a course evaluation after the examination. The evaluation is fully web-based and anonymous. The form to be filled will be made available

Results from earlier years: spring 2011 , spring 2012

Literature

The main book will be

M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory, 1995 (ISBN 0201503972), chapter 1-6

As side-literature, any of the following books can be recommended:

F. Mandl, G. Shaw, Quantum Field Theory
T. Banks, Modern Quantum Field Theory

Other material

Here you can find the FORM program and here is a program for calculating the leading order contribution to F2 in QED Here you can find video recordings of QFT lectures given by Sidney Cooleman at Harvard.

Questions

Please contact Johan Rathsman, Johan.Rathsman (at) thep.lu.se, 046-2223495

Introduction to Quantum Field Theory FYTN10, 7.5 hp Spring 2013