Quantum Field Theory 2027 Part II

Spring 2027: 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 include discussion from the following references

Rob Leigh’s lecture notes on QFT

“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 course website and Brightspace to post course announcements, homework, references, and further discussions. If you plan to attend the class, please ensure you receive notifications from Brightspace. All lectures will be recorded and posted on YouTube.

Homework:

The homework problems will be assigned in class and are due on Brightspace two weeks after they are posted.

Syllabus:

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

Non-Local Observables and Hidden Symmetry in Classical Field Theory

2) Non-local observables in field theory

• Lecture 3: Global symmetries and local algebras
• Lecture 4: Non-local operators and superselection sectors
• Problem Set 6
• Lecture 4′: Higher form symmetries

3) Symmetry-breaking in field theory

• Lecture 5: Symmetry-breaking and effective action
• Lecture 6: Global Spontaneous Symmetry-breaking
• Lecture 7: Spontaneous Symmetry-breaking in Gauge Theories

Renormalization: Integrating Fluctuations and Scale-dependence

1) Integrating Thermal Fluctuations

• Lecture 1: Self-similarity, Random Walk, and Renormalization
• Lecture 2: Langevin and Fokker-Planck equation
• Lecture 2′: Path-integral approach to Fokker-Planck equation
• Problem set 1

1) Renormalized Perturbation Theory and Effective Actions

• Lecture 3: Overview and power counting
• Lecture 4: Renormalized perturbation theory I
• Lecture 5: Renormalized perturbation theory II
• Lecture 6: Renormalized QED, vacuum polarization
• Lecture 7: Renormalized QED, Fermion self-energy
• Lecture 8: Renormalized QED, Vertex correction
  Problem Set 1
• Lecture 9: Effective actions I
• Lecture 10: Effective actions II
  Problem Set 2

2) Renormalization Group Flow

• Lecture 11: Wilsonian renormalization
• Lecture 12: Renormalization group flow
• Lecture 13: Callan-Symanzik equations
• Lecture 14: Renormalization of local operators and critical exponents
• Lecture 15: Wilson-Fisher fixed point
• Lecture 16: Nonlinear sigma model
• Problem Set 3
  Lecture 16′: Exact RG (see Lecture 13)

Gauge Theories and Nonlocal Observables

3) Non-local observables in quantum field theory

• Lecture 21: Global symmetries and local algebras
• Lecture 22: Non-local operators and superselection sectors
• Problem Set 6
• Lecture 22′: Higher form symmetries

5) Quantization of Non-Abelian Gauge Theories

• Lecture 17: Faddeev-Popov Lagrangian
• Lecture 18: Non-Abelian gauge theory at one loop
• Lecture 19: Asymptotic freedom
• Lecture 20: Confinement
• Problem Set 5

7) Hidden symmetry: Spontaneous symmetry breaking and Anomaly

• Lecture 23: The Higgs mechanism
• Lecture 24: Quantization of spontaneously broken gauge theories I
• Problem Set 7

8) Anomalies

• Lecture 25: Chiral Anomaly
• Lecture 25′: Scale Anomaly

9) Standard Model of Particle Physics

• Lecture 26: Particle Content of Standard Model
• Lecture 27: Spectrum, Higgs and Strong Interactions
• Lecture 28: Electroweak Interactions
• Lecture 29: Anomaly Cancellation in Standard Model
• Problem Set 8

10 ) Modern Topics

• Lecture 30: Operator Product Expansion
• Lecture 31: Entanglement in Quantum Field Theory

Special Topics

1. Operator Product Expansion
   Lecture 32: Operator Product Expansion in QFT
   Lecture 33: Operator Product Expansion in Conformal Field Theory
2. Theta-angle and Instantons
   Lecture 34: Magnetic Monopoles and Theta-Angle
   Lecture 35: Theta-Term and Instantons
3. Large N Expansion
   Lecture 36: Large N part I
   Lecture 37: Large N part II