Physics 721: Quantum Field Theory I
Fall 2023

Instructor: Josh Erlich
Small Hall rm 332B
Office Phone: 757-221-3763
Email: erlich@physics.wm.edu

Topics to be covered:

Review of Relativistic Quantum Mechanics


• Dirac's theory of the electron
• Relativistic covariance of the Dirac equation




Classical Field Theory


• Lagrangian and Hamiltonian densities
• Euler-Lagrange equation
• Symmetries and conservation laws
• Fields as collections of harmonic oscillators




Quantum Field Theory

• Canonical quantization
• Spin vs. statistics
• Quantum Electrodynamics
• Scattering theory and particle decays
• Perturbation theory and Feynman diagrams
• Intro to radiative corrections

Examples will be taken mainly from particle physics, but may also include condensed matter and atomic physics.

Course requirements and grade:

• Problem sets (70%)
• Take home final exam (30%)

Grade: A 93-100, A- 88-93, B+ 83-88, B 78-83, B- 73-78, C+ 68-73, C 63-68, C- 58-63, D+ 53-58, D 48-53, D- 43-48, F <43

Problem sets:

Reading material:

• Text:  M. Peskin and D. Schroeder, An Introduction to Quantum Field Theory, a widely used textbook

• Also recommended:
  • Ramond, Field Theory: A Modern Primer, a favorite of the PHYS 722 instructor.
  • M. Schwartz, Quantum Field Theory and the Standard Model, an excellent, more modern textbook
  • A. Zee, Quantum Field Theory in a Nutshell, a more-conceptual textbook with lots of good handwavy discussions
  • S. Weinberg, The Quantum Theory of Fields, not a good first textbook, but a must-read for QFT practitioners
  • David Tong's lecture notes, including links to Sydney Coleman's notes and other references. I encourage you to read both Tong's and Coleman's notes.
  • Complex variables cheat sheets

Lecture Notes:

Lecture Notes 1: What is quantum field theory? Relativistic QM and the Dirac equation.
Lecture Notes 2: Electromagetic interactions of the relativistic electron
Lecture Notes 3: Lorentz Invariance, Tensors
Lecture Notes 4: Lorentz covariance of the Dirac equation
Lecture Notes 5: Classical Field Theory
Lecture Notes 6: More Classical Field Theory
Lecture Notes 7: Canonical Quantization
Lecture Notes 8: Hamiltonian, Momentum, and Particle States
Lecture Notes 9: Feynman Propagator, Antiparticles and Causality
Lecture Notes 10: Plane-wave solutions to Dirac Equation, Dirac field bilinears
Lecture Notes 11: Quantization of the Dirac Field
Lecture Notes 12: Quantization of the Dirac Field: Part 2
Lecture Notes 13: Electrons and positrons: Energy, momentum, angular momentum, and charge
Lecture Notes 14: Quantum Electrodynamics
Lecture Notes 15: Scattering Theory
Lecture Notes 16: Wick's theorem
Lecture Notes 17: Feynman Diagrams
Lecture Notes 18: More Feynman Diagrams
Lecture Notes 19: Loops, Spin/polarization sums and averages
Lecture Notes 20: Cross Sections and Decay Rates

Problem Sets:
Problem Set 1 (pdf), due Monday, September 18. Solutions
Problem Set 2 (pdf), due Monday, September 25. Solutions
Problem Set 3 (pdf), due Monday, October 2. Solutions
Problem Set 4 (pdf), due Monday, October 9. Solutions
Problem Set 5 (pdf), due Monday, October 16. Solutions
Problem Set 6 (pdf), due Monday, October 23. Solutions
Problem Set 7 (pdf), due Monday, October 30. Solutions
Problem Set 8 (pdf), due Monday, November 6. Solutions
Problem Set 9 (pdf), due Monday, November 13. Solutions
Problem Set 10 (pdf), due Monday, December 4. Solutions

Final exam:
Final exam (pdf)