Fall 2026: PHYS662
Tue-Thu 1:30 pm – 2:45 pm at PHYS201.
The lecture videos are posted on YouTube here. The syllabus, lecture notes, and homework are also posted here. We will be using Brightspace.
Prerequisites: Advanced Quantum Mechanics and Statistical Physics.
Course Description: In this course, we will not have a textbook, but in almost all lectures, we will use parts of these textbooks and online resources:
“Quantum Theory of Fields, Volume 1” Weinberg
“An Introduction to Quantum Field Theory” Peskin and Schroeder
“Quantum Field Theory” Mark Srednicki
Rob Leigh’s lecture notes on QFT
David Tong’s lectures on Quantum Field Theory
Daniel Harlow’s lectures on Quantum Field Theory
McGreevy’s lecture notes on Particles and Fields
Sydney Coleman’s lecture notes on QFT
“Mathematical Theory of Quantum Fields” Huzihiro Araki
We will use the Slack application to post course announcements, reports, discuss ideas, and share exciting papers we have come across. All lectures will be recorded and posted on YouTube.
Homework:
The homework problems will be assigned in class and have to be submitted on Brightspace within two weeks after the lecture. The TA for the course is Yu-Shan Chang.
Syllabus:
Click on the lecture to download the lecture notes. The syllabus is subject to change as the course progresses.
1) What is QFT and Why?
- Lecture 1: From classical particles to classical fields (Statistical field theory)
Slides. Lecture Notes - Lecture 2: From quantum particles to quantum fields (Quantum field theory)
Slides. Lecture Notes - Lecture 3: From coupled atoms to an emergent quantum field (Quantum sound and phonons)
Slides. Lecture Notes - Lecture 4: Review of Symmetries and Groups
Lecture Notes - Problem set 1
Locality and Symmetry in Classical Field Theory
2) Locality: Action Principle
- Lecture 5: Action Principle, Lagrangians and Locality
Lecture Notes - Lecture 6: A few examples
Lecture Notes - Problem set 2
3) Symmetry: Conserved Charges
- Lecture 7: Symmetries and Noether’s theorem
Lecture Notes - Lecture 8: Lie Groups, Lie Algebras and their Representations
Lecture Notes - Lecture 9: Spin, Tensor products, and Quantum Symmetries
Lecture Notes - Lecture 10: Projective representations and Algebra of Charges
Lecture Notes
Problem set 3
4) What is a Particle: Representations of Lorentz and Poincaré groups
- Lecture 11: Representations of the Lorentz Group
Lecture Notes - Lecture 12: Spinors of the Lorentz group
Lecture Notes - Lecture 13: Lagrangian for spinors
Lecture Notes - Lecture 14: Single Particle States
Lecture Notes - Problem set 4
Free (Gaussian) Quantum Fluctuations
5) Quantum Fluctuations: Canonical Quantization, Many particles all at once!
- Lecture 15: Canonical quantization of free fields
Lecture Notes - Lecture 16: Causality and Propagators
Lecture Notes - Problem Set 5
6′) Correlation functions and local algebra of quantum fields
- Lecture 16′: Algebra of Local Observables in QFT
- Lecture 16”: Correlation functions and Wightman axioms
6) Path-integral quantization
- Lecture 17: Path-integrals in Quantum Mechanics I
Lecture Notes - Lecture 18: Path-integrals in Quantum Mechanics II
Lecture Notes - Lecture 19: Path-integrals for free scalar field
Lecture Notes - Lecture 20: Path-integral for fermionic fields
Lecture Notes - Problem Set 6
Perturbative Interactions: Non-Gaussianities
7) Perturbation theory and Feynman diagrams
- Lecture 21: Interactions in path integrals and Feynman rules
Lecture Notes - Lecture 22: One-loop corrections in scalar field theory
Lecture Notes - Problem Set 7
8) Particles and Scattering Theory
- Lecture 23: Multiparticle states and scattering
Lecture Notes - Lecture 24: Decay rates and cross-section
Lecture Notes - Lecture 25: Scattering matrices from correlation functions
Lecture Notes - Problem Set 8
9) Quantum Electrodynamics
- Lecture 26: Quantization of the electromagnetic field
Lecture Notes - Lecture 27: Quantum electrodynamics
Lecture Notes - Lecture 28: Loop corrections to propagators
Lecture Notes - Lecture 29: Loop corrections to a vertex
Lecture Notes - Problem Set 9
