Quantum Field Theory 2025 Part II

Spring 2025: PHYS 663

Tue-Thu 4:30 pm – 5:45 pm at PHYS331. The videos of the lectures are posted on YouTube here. The lectures will also be live on Zoom.

Prerequisites: Quantum Field Theory Part I (PHYS 662).

Course Description:
This course is part II of a year-long Quantum Field Theory (QFT) course. We will continue with the Lagrangian formulation of QFT. The lecture notes will mostly follow

Rob Leigh’s lecture notes on QFT

however, they will include many discussions from other references:

“An Introduction to Quantum Field Theory” Peskin and Schroeder

In almost all lectures, we will use parts of other textbooks and online resources such as

“Quantum Theory of Fields, Volume 1” Weinberg

“Quantum Theory of Fields, Volume 2” Weinberg

“Quantum Field Theory” Mark Srednicki

David Tong’s lectures on Quantum Field Theory

David Tong’s lectures on Gauge Theories

“The Standard Model A Primer” Cliff Burgess and Guy Moore

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 application Slack to post course announcements, and reports, discuss ideas, and share exciting papers we have come across. If you plan to attend the class please email me and I will add you to the course channel on Slack. All lectures are going to be recorded and posted on YouTube.

Homework:

The homework problems will be assigned in class and have to be submitted on Slack up to two weeks after the lecture. The TA for the course is Shoy Ouseph.

Syllabus:

Click on the lecture to download the lecture notes. The syllabus is subject to change as the course progresses.

Scale-dependence

1) Renormalized Perturbation Theory and Effective Actions

• Lecture 1: Overview and power counting
• Lecture 2: Renormalized perturbation theory I
• Lecture 3: Renormalized QED I
• Lecture 4: Renormalized QED II
  Problem Set 1
• Lecture 5: Effective actions I
• Lecture 6: Effective actions II
  Problem Set 2

2) Renormalization Group Flow

• Lecture 7: Wilsonian renormalization
• Lecture 8: Renormalization group flow
• Lecture 9: Callan-Symanzik equations
• Lecture 10: Renormalization of local operators and critical exponents
• Lecture 11: Wilson-Fisher fixed point
• Lecture 12: Nonlinear sigma model
• Problem Set 3
  Lecture 12′: Exact RG (see Lecture 13)

Gauge Theories and Nonlocal Observables

3) Non-local observables in classical field theory

• Lecture 13: Gauge redundancies
• Lecture 14: Where do gauge theories come from?
• Problem set 4
  Lecture 14′: Higher form symmetries

5) Quantization of Non-Abelian Gauge Theories

• Lecture 15: Faddeev-Popov Lagrangian
• Lecture 16: Non-Abelian gauge theory at one loop
• Lecture 17: Asymptotic freedom
• Lecture 18: Confinement
• Problem Set 5

6) Non-local observables in quantum field theory

• Lecture 19: Global symmetries and local algebras
• Lecture 20: Non-local operators and superselection sectors
• Problem Set 6

7) Hidden symmetry: Spontaneous symmetry breaking

• Lecture 21: The Higgs mechanism
• Lecture 22: Quantization of spontaneously broken gauge theories I
• Problem Set 7

8) Anomalies

• Lecture 23: Chiral Anomaly
  Lecture 23′: Scale Anomaly

9) Standard Model of Particle Physics

• Lecture 24: Particle Content of Standard Model
• Lecture 25: Spectrum, Higgs and Strong Interactions
• Lecture 26: Electroweak Interactions
• Lecture 27: Anomaly Cancellation in Standard Model
• Problem Set 8

10 ) Modern Topics

• Lecture 28: Operator Product Expansion
• Lecture 29: Entanglement in Quantum Field Theory

Special Topics

1. Operator Product Expansion
   Lecture 30: Operator Product Expansion in QFT
   Lecture 31: Operator Product Expansion in Conformal Field Theory
2. Theta-angle and Instantons
   Lecture 32: Magnetic Monopoles and Theta-Angle
   Lecture 33: Theta-Term and Instantons
3. Large N Expansion
   Lecture 34: Large N part I
   Lecture 35: Large N part II