PHY 513, Fall '09
QUANTUM FIELD THEORY I

Lecturer: Finn Larsen
 

 
LECTURES
Tue+Thu 2.30-4pm, 4404 Randall.
OFFICE HOURS
 Monday 1-2, 3481 Randall.
TEXTBOOK
 Peskin and Schroeder, 'An Introdution to Quantum Field Theory";
Westview Press 1995.



COURSE DESCRIPTION

When quantum mechanics is combined with special relativity, the number of
particles in a system is no longer conserved: creation and annihilation becomes possible.
The number of excitations can be arbitrarily large and it is convenient to describe the
states of relativistic quantum theory in terms of quantum fields. These are quantum
versions of the sort of fields that are familar from electromagnetism. The purpose of this
course is to develop relativistic quantum field theory systematically.

Quantum field theory is an indispensible language in many branches of physics. The main
focus of this course will be on applications to particle physics but in the process we will also
discuss radiative corrections (important in atomic physics) and the systematic theory of
photons (central to quantum optics).  Very similar concepts and formalism apply to quantum many-body
theory (condensed matter physics) and to thermal fluctuations in critical phenomena (statistical
mechanics).

The great diversity of possible applications of quantum field theory is surprising at first but,
as the subject gets developed, it becomes clear that this is no accident. Ultimately this
understanding of universality may be the most profound lesson of quantum field theory.

The first semester of the course (PHY513) is a self-contained introduction to Quantum
Electrodynamics at the leading order. Some subjects are the Dirac equation, Feynman
diagrams, and path integrals. The second semester (PHY523) discusses renormalization
theory and its interpretation.


SYLLABUS
 


Week
 Lecture 1
 Lecture 2
 Problems
 Comments
September 8-11
 Introduction (chap 1, Sec 2.1)
 Classical Field Theory (sec 2.2)
 HW1.pdf
Jackson 11.6+7+10 covers relativity
September 14-18
 The Quantum Field (sec 2.3)
Spacetime Interpretation of Quantum Fields (sec 2.4, pp25-29)
HW2.pdf

 Goldstein chap 12 covers classical field theory.
September 21-25
 Green's Functions (sec 2.4, pp29-33)
 The Lorentz Group (sec 3.1)
HW3.pdf
Sep.28-oct. 2
 The Dirac Equation (sec 3.2)
 Solutions of the Dirac Equation (sec 3.3)
HW4.pdf
October 5 - 9
 Quantization of the Dirac Field (sec 3.5)
 Parity Transformations (sec 3.4 pp. 49-51; sec 3.6 pp 64-67)
HW5.pdf
October 12-16
 C, T, CPT (sec 3.6, pp 67-71)
 Interactions in QFT (sec 4.2)
HW6.pdf

HW6 due thu oct 22.
October 19-23
No class: fall break
 Feynman Diagrams for Correlators (sec 4.3+4.4)

Midterm due tue oct 27.
October 26-30
The S-matrix and Cross-sections (sec 4.5)
Feynman Diagrams for Amplitudes (sec 4.6) 
 HW7.pdf
November 2-6
Yukawa Theory (sec 4.1+sec 4.7 to p 120)
Quantum Electrodynamics (sec 4.7 pp 121-; sec 4.8)
HW8.pdf
November 9-13
 Electron-Positron Annihilation (sec 5.1)
Helicity Structure (sec 5.2)
 HW9.pdf
November 16-20
Crossing Symmetry (sec 5.4) Compton Scattering (sec 5.5) HW10.pdf
November 23-27
Feynman Rules from Path Integrals (sec 9.1) No class: thanksgiving
 HW11.pdf
Nov. 30- Dec 4
Feynman Rules from Path Integrals (sec 9.2)
Path Integrals for Fermions (sec 9.5)
 
HW12.pdf
December 7 - 11
Quantization of the EM field (sec 9.4) Symmetries in Quantum Field Theory (sec 9.6)
Final due mon dec. 14.

 


HOMEWORK


Each week you should:
1) Read the material indicated in the syllabus above under each of the two lectures. You are supposed to read
ALL the material indicated, also when it was not covered in class. 
2) Check ALL the formulae in the sections you are reading. It is good practice for you to do the algebra. Also, it will often be useful to focus on concepts in class, leaving the computations for homestudy. This puts some RESPONSIBILITY on you, the student.
3) Do the assigned problems. You are encouraged to work together.
HWs linked above are due on the tuesday after the week listed.
Beware that I may adjust the HW until about a week before due date.
4) Submit written solutions to the problems tuesday in class.



EVALUATION


The GRADE will be determined from:
1) HOMEWORK  (1/3).
2) MIDTERM (1/3). Take-home exam available fri oct 23, due thu oct 27 in class
3) FINAL (1/3). Take-home exam available thu dec 10, due mon dec 14.
The weigthings are preliminary and may change slightly.


The exams will include questions of the form:
1) Problems already discussed in class.
2) Checking formulae in the book.
3) New problems about central issues discussed repeatedly in class.
If you keep up with the homework (as spelled out above) the exams will be extremely reasonable;
however, they will be very hard work if you have not kept up.

ALTERNATE TEXTBOOKS


There are NUMEROUS textbooks that are relevant for this course. Each has slightly different emphasis
and students have different preferences. The following is a list to some of the books that you may consider
as ressources:

1) Peskin and Schroeder: "an Introduction to Quantum Field Theory".
This is probably the most popolur book for courses like this at US graduate schools and it is the book we
use. It is fairly pedagogical and works out examples in much detail.
Drawbacks: rather long, somewhat chatty at times, and focussed on particle physics.

2) Weinberg:"Quantum Theory of Fields vol I+II".
The authoritative reference. Insightful, often original, always right; has the answer to all questions.
Drawbacks: too difficult for a first course on QFT and too long for a one-year course.

3) Itzykson and Zuber: "Relativistic Quantum Field Theory".
Very clear and a good alternative to PS which covers many of the same subjects with a similar
philosophy. Many worked examples. Good Reference book.
Drawbacks: spinors introduced through old-fashioned relativistic quantum mechanics; sold out.

4) Zee: "Quantum Field Theory in a Nut-shell".
Conceptual with lots of entertaining anecdotes. Applications are to many fields of study including
condensed matter physics.
Drawback: too little formalism for a primary text.

 5) Ryder: Quantum Field Theory.
Relatively elementary. Introducing everything using path-integrals.
Drawback: a lot less material than PS, even more emphasis on particle physics.

6) Mandl and Shaw: Quantum Field Theory.
A viable alternative to PS. More concise and to the point.
Drawbacks: Fewer examples and less discussion.

7) Ramond: Quantum Field Theory, a modern Primer.
A good introductory book, fully based on path integrals.
Drawback: path integrals can be difficult for the beginner.
8) Srednicki: Quantum Field Theory.
A good new book at the right level for a course like this.
Recommended as supplementary reading.