Quantum Field Theory I

Fall 2023: PHYS 662

Tue-Thu 1:30 pm – 2:45 pm on Zoom. The videos of the lectures are posted on YouTube here. If you have signed up for the course, or planning to sign up please send me an email so that I can invite you to the SLACK channel.

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 particles to fields
• Lecture 2: Quantum sound (Phonons)
• Problem set 1

Classical Field Theory

2) Actions: Principle of Locality

• Lecture 3: Action Principle, Lagrangians and Locality
• Lecture 4: A few examples
• Problem set 2

3) Conserved Charges: Principle of Symmetry

• Lecture 5: Symmetries and Noether theorem
• Lecture 6: Global symmetries, Lie Groups and Lie algebras
• Lecture 7: Representations of Lie algebras
  Problem set 3

4) Gauge Redundancies and Nonlocal observables

• Lecture 8: Gauge redundancies
• Lecture 9: Where do Gauge Theories come from?
• Problem set 4

5) What is a Particle: Poincare Group and Representations

• Lecture 10: Representations of the Lorentz Group
• Lecture 11: Weyl, Majorana and Dirac Spinors
• Lecture 12: Particle States
• Problem set 5

Quantization

6) Canonical Quantization: Many particles all at once!

• Lecture 13: Free Relativistic Scalar Field Theory
• Lecture 14: Free Dirac Fermion Field
• Lecture 15: Causality and Propagators
• Problem Set 6

7) Path-integral Quantization

• Lecture 16: Path-integrals in Quantum Mechanics I
• Lecture 17: Path-integrals in Quantum Mechanics II
• Lecture 18: Path-integrals for free scalar field
• Lecture 19: Interactions in path-integrals and Feynman rules
• Problem Set 7
• Lecture 20: Path-integral for fermions
• Lecture 21: Scattering matrices
• Lecture 22: Feynman rules for quantum electrodynamics
• Lecture 23: Cross Section and decay rates
• Problem Set 8

8) Quantum Electrodynamics

• Lecture 24: Path-integrals for quantum electrodynamics
• Lecture 25: Loop amplitudes in QED (Vacuum polarization Part I)
• Lecture 26: Loop amplitudes in QED (Vacuum polarization Part II)
• Lecture 27: Loop amplitudes in QED (Fermion self-energy and vertex correction I)
• Lecture 28: Loop amplitudes in QED (vertex correction II)
• Problem Set 9

Lecture 29: Review of QFT I