PHY 523, Winter '10

Lecturer: Finn Larsen


Mon+Wed 1-2.30pm, Randall 4404.
?? in Randall 3481.
Peskin and Schroeder, 'An Introdution to Quantum Field Theory";
Westview Press 1995.


This course continues the study of  quantum field theory initiated in PHY 513.

We develop the quantum theory of radiative corrections. Technically, the central concept is
loops in quantum field theory and their divergences. Physically, we interpret loops in terms
of the renormalization group. More broadly, we discuss quantum field field theory as an
effective theory.

Although we will develop quantum field theory primarily in the contect of particle physics the
techniques are highly relevant also in AMO, in statistical mechanics (particularly in critical
phenomena), and also in many body physics.

The last 7 lectures (sec 14, 15, 16, 19) form the technical basis for the standard model of particle
physics. Those students interested in applications to other fields can replace those last lectures with
a group project (talk to me for more detail). 



Lecture 1
Lecture 2
Jan. 4-8
(semester begins wednesday)
Soft Bremsstrahlung (sec 6.1)

Jan. 11-15
The Electron Vertex Function I (sec 6.2) The Electron Vertex Function II (sec 6.3) HW1.pdf

Jan. 18-22


Infrared Divergences I (sec 6.4) HW2.pdf

Jan. 25-29
Infrared Divergences II (sec 6.5)
The Electron Self-Energy (sec 7.1)

Feb. 1-5
The LSZ Reduction Formula (sec 7.2).
The Optical Theorem (sec 7.3) HW4.pdf

Feb. 8-12 
The Ward-Takahashi-Identity (sec 7.4) Vacuum Polarization (sec 7.5+app. A4) HW5.pdf

Feb. 15-19 
Charge Renormalization (sec 7.5) Counting of Ultraviolet Divergences (sec 10.1) HW6.pdf Chapter 8 is strongly recommended.
Feb 22- 26
Renormalized Perturbation Theory (sec 10.2) Renormalization of QED (sec 10.3)

March 1-5

Winter Break
March 8-12
The Renormalization Group Flow (sec 12.1)   The Callan-Symanzik Equation (sec 12.2) HW7.pdf

March 15-19
Evolution of Coupling Constants (sec 12.3) Effective Field Theory and Renormalization of Local Operators (sec 12.4) HW8.pdf
Mar. 22-26
Critical Phenomena (Sec 8+12.5)
Non-Abelian Gauge Invariance (sec 15.1+15.2)

Mar. 29- Apr. 2
Quantum Yang-Mills Theory (sec 16.1-16.3)
Asymptotic Freedom (parts of sec 16.5, 16.7)

Apr. 5 - Apr. 9
Deep Inelastic Scattering (sec 14, 17.3)
Parton Evolution I (parts of sec 17.2, 17.4, 17.5)

HWs for the course due on wed. apr. 7
Apr. 12-16
Parton Evolution II (sec 17.5, 17.6)
Anomalies I (sec 19.1+19.2 to p.661)

Final Exam available thu. apr. 15, due mon. apr 19.
Apr. 19-23
Anomalies II (sec 19)



For those students less interested in particle physics the last 8 lectures can be replaced by a project adapted to individual interest. For example a small group of students could study chapter 11/13 (effective potentials and critical phenomena, essential in cosmology and statistical mechanics), and give a presentation on parts of this material.


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 BEFORE the problem session. You are encouraged to work together.
4) Submit written solutions to the problems in early april.


The GRADE will tentatively be determined from:
1) Homework (1/2).
2) Final (1/2).


There are NUMEROUS textbooks on QFT. Each has slightly different emphasis and people
have different preferences. The following is a very incomplete list of recommended books that
you may consider as ressources:

1) Peskin and Schroeder: "an Introduction to Quantum Field Theory".
This is probably the most popular textbook for QFT courses 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.
Drawback: too difficult for a first course on QFT (I think) and too long for a one-year course.

3) Itzykson and Zuber: "Relativistic Quantum Field Theory"
Very clear. A good alternative to PS which covers many of the same subjects with a similar

4) Landau+Lifshitz: Quantum Eletrodynamics,
Straight to the point. Many details on specific processes, including atomic and nuclear physics.
Drawback: terse.

5) Zee: "Quantum Field Theory in a Nut-shell".
Focus on concept. Lots of entertaining anecdotes. Applications to many fields of study including
condensed matter physics.
Drawback: too little formalism for a primary text.

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

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

8) 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.

9) Srednicki: Quantum Field Theory.
A good new book at the right level for a course like this.
Recommended as supplementary reading.