Introduction to Quantum Field Theory, FYTN10

Introduction to
Quantum Field Theory
FYTN10, 7.5 hp
Spring 2012

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 16 to March 20).

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 problem solving sessions.

Preliminary schedule

The course will start on January 16 and then continue with 2-4 sessions per week until March 20. The introductory meeting will be 10-12 on January 16 and then the lectures will be as follows with tentative subjects

Date	Time	Place	Subject	Peskin and Schroeder	Hand-in exercise
Mon 16/1	10-12	Sal NB	Introduction
Wed 18/1	13-15	Sal NB	Classical field theory, Noether's theorem	Chapter 2.1-2.2
Fri 20/1	13-15	Sal NB	Klein-Gordon field, causality and progator	Chapter 2.3-2.4 (7.1)
Tue 24/1	10-12	Sal NB	Perturbation theory and Correlation fcn's	Chapter 4.1-4.2
Wed 25/1	13-15	Sal NB	Problems chapter 2	-
Thu 26/1	10-12	Sal NB	Wick's theorem, Feynman diagrams	Chapter 4.3-4.4
Fri 27/1	13-15	Sal NB	Cross-sections	Chapter 4.5
Tue 31/1	10-12	Sal NB	S-matrix from Feynman diagrams	Chapter 4.6 (7.2)	nr 1 due
Thu 2/2	10-12	Sal NB	Dirac field, Weyl representation	Chapter 3.1-3.2
Tue 7/2	10-12	Sal NB	Problems chapter 4.1-4.6	-
Wed 8/2	13-15	Sal NB	Free particle solutions, Dirac bilinears	Chapter 3.3-3.4
Thu 9/2	10-12	Sal NB	Quantization of Dirac Field	Chapter 3.5
Fri 10/2	13-15	Sal NB	Discrete symmetries of Dirac Field	Chapter 3.6
Tue 14/2	10-12	Sal NB	Feynman rules for fermions	Chapter 4.7	nr 2 due
Thu 16/2	10-12	Sal NB	Yuakawa theory and QED	Chapter 4.8
Fri 17/2	13-15	Sal NB	e+e- -> mu+mu-: introduction	Chapter 5.1
Thu 23/2	10-12	Sal NB	Problems chapter 3 and 4	-
Fri 24/2	13-15	Sal NB	Problems chapter 3 and 4, cont'd if needed	-
Tue 28/2	10-12	Sal NB	e+e- -> mu+mu-: helicity structure	Chapter 5.2	nr 3 due
Wed 29/2	13-15	Sal NB	Non-relativistic limit, Crossing symmetry	Chapter 5.3-5.4
Thu 1/3	10-12	Sal NB	Compton scattering	Chapter 5.5
Fri 2/3	13-15	Sal NB	Bremsstrahlung and electron vertex correction	Chapter 6.1-6.2
Tue 6/3	10-12	Sal NB	Problems chapter 5	-
Thu 8/3	10-12	Sal NB	Electron vertex correction: UV and infrared divergences	Chapter 6.3-6.4
Fri 9/3	13-15	Sal NB	Summation and interpretation of infrared divergences	Chapter 6.5	nr 4 due
Tue 13/3	10-12	Sal NB	Problems chapter 6	-
Fri 16/3	13-15	Sal NB	Question and Answer session
Mon 19/3	-	-	Oral exams
Tue 20/3	-	-	Oral exams

Problems 8may still be utpdated)

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
Download problems for chapter 6 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 examination

The starting point for the oral examination 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.

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

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

Questions

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