Quantum Field Theory Part I

Fall 2024: PHYS662

Tue-Thu 1:30 pm – 2:45 pm at PHYS201.
The lectures’ videos are posted on YouTube here. The syllabus, lecture notes, and homework are also posted here.

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

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 Derek Ping.

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
• Lecture 2: From quantum particles to quantum fields
• Lecture 3: 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 theorem
• Lecture 7: Global symmetries, Lie Groups, and Representations
• Lecture 8: Representations of Lie Groups I
• Lecture 9: Representations of Lie Groups II
• Extra: Representation of SO(N)
  Problem set 3

4) What is a Particle: Lorentz and Poincare group and their representations

• Lecture 10: Representations of the Lorentz Group
• Lecture 11: Weyl Spinors
• Lecture 12: Majorana and Dirac Spinors
• Lecture 13: Particle States
• Problem set 4

Quantization

5) Canonical Quantization: Many particles all at once!

• Lecture 14: Free Relativistic Scalar Field Theory
• Lecture 15: Free Dirac Fermion Field
• Lecture 16: Causality and Propagators
• Problem Set 5

6) Correlation functions and local algebra of Quantum Fields

• Lecture 17: Algebra of Local Observables in QFT
• Extra: Correlation functions and Wightman axioms

7) Path-integral Quantization: Free fields

• Lecture 18: Path-integrals in Quantum Mechanics I
• Lecture 19: Path-integrals in Quantum Mechanics II
• Lecture 20: Path-integrals for free scalar field
• Lecture 21: Path-integral for fermions
• Problem Set 6

8) Path-integral Quantization: Interactions

• Lecture 22: Interactions in path-integrals and Feynman rules
• Lecture 23: Scattering matrices
• Lecture 24: Decay Rates and Cross-section
• Problem Set 7

9) Epilogue: Quantum Electrodynamics

• Lecture 25: Quantization of electromagnetic field
• Lecture 26: Quantum Electrodynamics
• Lecture 27: Loop amplitudes in QED (vacuum polarization I)
• Lecture 28: Loop amplitudes in QEC (vacuum polarization II)
• Lecture 29: Loop amplitudes in QED (fermion self-energy, vertex correction I)
• Lecture 30: Loop amplitudes in QED (fermion self-energy, vertex correction I)