PHY 523, Winter '09
QUANTUM FIELD THEORY II

Lecturer: Finn Larsen
 

 
LECTURES
Mon+Wed 1-2.30pm, ??.
DISCUSSION
 Tuesday, 4-5.30 in Randall 3481.
TEXTBOOK
 Peskin and Schroeder, 'An Introdution to Quantum Field Theory";
Westview Press 1995.



COURSE DESCRIPTION


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). 


SYLLABUS
 

Week
 Lecture 1
 Lecture 2
 Problems
 Comments
Jan. 5-9
 NO LECTURE
(semester begins wednesday)
 Soft Bremsstrahlung (sec 6.1)


Jan. 12-16
 The Electron Vertex Function I (sec 6.2) The Electron Vertex Function II (sec 6.3) HW1.pdf
Jan. 19-23
 Infrared Divergences I (sec 6.4) Infrared Divergences II (sec 6.5) HW2.pdf

Mon Jan 19 is MLK day: we will have a make up lecture that day.
Jan. 26-30
 The Electron Self-Energy (sec 7.1)
 The LSZ Reduction Formula (sec 7.2).
 HW3.pdf
Feb. 2-6
 The Optical Theorem (sec 7.3)
 The Ward-Takahashi-Identity (sec 7.4) HW4.pdf
Feb. 9-13 
Vacuum Polarization (sec 7.5+app. A4) Charge Renormalization (sec 7.5) HW5.pdf

 Chapter 8 is strongly recommended.
Feb. 16-20 
Counting of Ultraviolet Divergences (sec 10.1) Renormalized Perturbation Theory (sec 10.2) HW6.pdf
Feb 23- 27
NO LECTURE NO LECTURE

Winter Break
March 2-6
Renormalization of QED (sec 10.3) The Renormalization Group Flow (sec 12.1)


March 9-13
The Callan-Symanzik Equation (sec 12.2) Evolution of Coupling Constants (sec 12.3)   HW7.pdf
March 16-20
Effective Field Theory and Renormalization of Local Operators (sec 12.4) Critical Phenomena (Sec 8+12.5) HW8.pdf
  
Mar. 23-27
 Non-Abelian Gauge Invariance (sec 15)
Non-Abelian Gauge Invariance (sec 15)
HW9.pdf
Mar. 30- Apr. 3
Asymptotic Freedom (sec 16)
 Non-Abelian Quantum Theory (sec 16)
 HW10.pdf
Apr. 6 - Apr. 10
 Non-Abelian Quantum Theory (sec 16)
 Spontaneous Symmetry Breaking (Sec 11.1)
HWs for the course due on wed. apr. 8
Apr. 13-17
NO LECTURE
 NO LECTURE
Final Exam available thu. apr. 16, due mon. apr 20.
Apr. 20-24
 Anomalies (sec 19) Anomalies (sec 19)
Semester ends tuesday, we have make up lecture on wednesday.

 

PROJECT 


There will be an extended HW in the week before spring break. This is the projected listed as project 1 in PS, the computation of radiative QCD corrections in a realistic setting.

For those students less interested in particle physics that project can be replaced by another relevant project. Similarly the last
7 lectures can be replaced by a project adapted to individual interest. For example one may study chapter 11/13 (effective potentials
and critical phenomena, essential in cosmology and statistical mechanics). 


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



EVALUATION

The GRADE will tentatively be determined from:
1) Homework (1/4).
2) Project (1/4).
3) Final (1/2).





ALTERNATE TEXTBOOKS



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
philosophy.

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.
Drawback: 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.