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 reinforcing non-introductory topics like loop calculations, UV and IR 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, and sometimes dip into my own introductory QFT lecture notes. Other references sometimes used in class are the Appendices of my book Introduction to Effective Field Theory.

See below for procedural course information and the course syllabus when it is taught as a full-term course. When taught as a half-term module I would normally aim to cover sections 1, 2, 3 and 5, though these can be tweaked depending on class interest.


  1. Which Fields for Which Particles?
    1. Relativity + QM = Antiparticles, Spin-Statistics & CPT
    2. Spins Zero and Half
    3. Spin One: Why Gauge Invariance?
  2. Quantum Electrodynamics
    1. Feynman Rules and the Miracle of Lorentz Invariance
    2. Canonical Quantization
    3. Path Integral Quantization
  3. Loop Calculations
    1. Vacuum Polarization
    2. Regularization and Renormalization
    3. Anomalous Magnetic Moments
  4. Nonperturbative Methods
    1. Interaction/Heisenberg Picture and Low’s Theorem
    2. Lehman-Kallen Representation
    3. LSZ Reduction and Pole-ology
  5. Infrared Divergences
    1. The Bloch-Nordsieck and KLN Theorems
    2. The Renormalization Group
  6. Anomalies
    1. Triangle Graphs
    2. The Axial U(1) Problem
    3. Neutral Pion Decay
    4. The Standard Model


The class is offered both in person and online. In the first instance classes will be held in the ALICE room at Perimeter Institute each Tuesday from Nov 1 to Dec 6, 2022 from 10:00 – 11:30 and again from 2:30 – 4:00. Both sessions are on the same day to facilitate in-person attendance by those not in Waterloo. The location will be revisited depending on the numbers enrolled.

Assignment and Take-Home Test

This term’s assignment/take-home exam can be found here. It is due midnight on the evening of Sunday Dec 18 (a hard deadline so I can mark things and submit the marks on time). It should be handed in as a pdf file with your name and student number (and University – UW, Mac etc) and emailed to me with the subject line “QED Final” so I can find it in my email. I will respond to each file acknowledging receipt as I receive it so if you have not heard from me in 24 hours after submitting please contact me.

Good luck!