Quantum Field Theory II

This course is aimed at graduate students who have already had a first exposure to quantum field theory. Its main focus is on loop calculations, divergences and renormalization, using Quantum Electrodynamics as the illustrative example.

Although I work from my own notes, I closely follow volumes I and II of Steven Weinberg’s textbook on Quantum Field Theory. See below for the course syllabus and detailed course information.


  1. Review of Free Fields1.1 Spin Zero
    1.2 Spin Half
    1.3 Spin One
  2. Quantum Electrodynamics2.1 Feynman Rules and the Miracle of Lorentz Invariance
    2.2 Canonical Quantization
    2.3 Path Integral Quantization
  3. Loop Calculations3.1 Vacuum Polarization
    3.2 Regularization and Renormalization
    3.3 Anomalous Magnetic Moments
  4. Nonperturbative Methods4.1 Interaction/Heisenberg Picture and Low’s Theorem
    4.2 Lehman-Kallen Representation
    4.3 LSZ Reduction and Pole-ology
  5. Infrared Divergences5.1 The Bloch-Nordsieck and KLN Theorems
    5.2 The Renormalization Group
  6. Anomalies6.1 Triangle Graphs
    6.2 The Axial U(1) Problem
    6.3 Neutral Pion Decay
    6.4 The Standard Model


The course TA is Yu-Xiang Gu, who holds office hours in room 480 at PI on Fridays from 1-3 pm.


The course work involves completing a number of assignments.

Since Quantum Field Theory is only really learned by doing, it is strongly recommended to work the assignments even if you only audit the course.

Take-Home Exam

The take home exam for this course is available here shortly before noon on Thursday October 19 2012. Solutions must be submitted by noon Friday October 20, 2012. This can be done either by putting it in my mailbox at PI; by giving it to me at PI in person; or by emailing it to me at cburgess@perimeterinstitute.ca (cced to Yu-Xiang at yuxianggu@gmail.com).

Needless to say, the purpose of the take home format is to give you more time, and you are on your honour not to get help from any other people or sources of information. Good luck!