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)
- Lecture 2: From quantum particles to quantum fields (Quantum field theory)
- Lecture 3: First example of a QFT – Quantum sound (Phonons)
- Problem set 1
Classical Field Theory
2) Actions: Principle of Locality
- Lecture 4: Action Principle, Lagrangians and Locality
- Lecture 5: A few examples
- Problem set 2
3) Conserved Charges: Principle of Symmetry
- Lecture 6: Symmetries and Noether’s theorem
- Lecture 7: Symmetries, Groups, and Representations
- Lecture 8: Lie Groups, Lie Algebras and their Representations
- Lecture 9: Projective representations, Algebra of Charges
Problem set 3
4) Non-local observables in classical field theory
- Lecture 10: Gauge redundancies
- Lecture 11: Where do gauge theories come from?
- Problem set 4
4) What is a Particle: Representations of Lorentz and Poincaré groups
- Lecture 12: Representations of the Lorentz Group
- Lecture 13: Spinors of the Lorentz group
- Lecture 14: Lagrangian for spinors
- Lecture 15: Single Particle States
- Problem set 4
5) Renormalization: Principle of Tamed Fluctuations
- Lecture 16: Self-similarity, Random Walk, and Renormalization
- Lecture 17: Langevin and Fokker-Planck equation
- Lecture 18′: Path-integral approach to Fokker-Planck equation
- Problem set 5
Quantization
6) Canonical quantization: Many particles all at once!
- Lecture 18: Free Relativistic Scalar Field Theory
- Lecture 19: Free Dirac Fermion Field
- Lecture 20: Causality and Propagators
- Problem Set 6
6′) Correlation functions and local algebra of quantum fields
- Lecture 18′: Algebra of Local Observables in QFT
- Lecture 18”: Correlation functions and Wightman axioms
7) Path-integral quantization
- Lecture 21: Path-integrals in Quantum Mechanics I
- Lecture 22: Path-integrals in Quantum Mechanics II
- Lecture 23: Path-integrals for free scalar field
- Problem Set 7
- Lecture 24: Interactions in path-integrals and Feynman rules
- Lecture 25: Path-integral for fermions
- Problem Set 8
8) Particles and Scattering Theory
- Lecture 26: Multiparticle states and scattering
- Lecture 27: Decay rates and cross-section
- Lecture 28: Scattering matrices from correlation functions
- Problem Set 9
9) Quantum Electrodynamics
- Lecture 29: Quantization of the electromagnetic field
- Lecture 30: Quantum electrodynamics
- Lecture 30′: Loops corrections to a vertex
- Problem Set 10
Nima Lashkari 