David Tong: Lectures on Quantum Field Theory
These lecture notes are based on an introductory course on quantum field theory, aimed at Part III (i.e. masters level) students. The full set of lecture notes can be downloaded here, together with videos of the course when it was repeated at the Perimeter Institute. Individual sections can be downloaded below.
- 0. Preliminaries:
- 1. Classical Field Theory:
Table of Contents; Introduction; Lagrangian Field Theory; Lorentz Invariance; Noether's Theorem and Conserved Currents; Hamiltonian Field Theory.
- 2. Canonical Quantization:
The Klein-Gordon Equation, The Simple Harmonic Oscillator; Free Quantum Fields; Vacuum Energy; Particles; Relativistic Normalization; Complex Scalar Fields; The Heisenberg Picture; Causality and Propagators; Applications; Non-Relativistic Field Theory
- 3. Interacting Fields:
Types of Interaction; The Interaction Picture; Dyson's Formula; Scattering; Wick's Theorem; Feynman Diagrams; Feynman Rules; Amplitudes; Decays and Cross Sections; Green's Functions; Connected Diagrams and Vacuum Bubbles; Reduction Formula
- 4. The Dirac Equation:
The Lorentz Group; Clifford Algebras; The Spinor Representation; The Dirac Lagrangian; Chiral Spinors; The Weyl Equation; Parity; Majorana Spinors; Symmetries and Currents; Plane Wave Solutions.
- 5. Quantizing the Dirac Field:
A Glimpse at the Spin-Statistics Theorem; Fermionic Quantization; Fermi-Dirac Statistics; Propagators; Particles and Anti-Particles; Dirac's Hole Interpretation; Feynman Rules
- 6. Quantum Electrodynamics:
Gauge Invariance; Quantization; Inclusion of Matter -- QED; Lorentz Invariant Propagators; Feynman Rules; QED Processes.
- Problem Sheet 1: Postscript  PDF Classical Field Theory
- Problem Sheet 2: Postscript  PDF Quantizing the Scalar Field
- Problem Sheet 3: Postscript  PDF The Dirac Equation
- Problem Sheet 4: Postscript  PDF Scattering Amplitudes
Quantum Field Theory on the Web
- Quantum Field Theory by Michael Luke.
- Fields by Warren Siegel.
- Quantum Condensed Matter Field Theory by Ben Simons
- Errata for the book by Peskin and Schroeder
Philip Tanedo, who took this course long ago, has put together a useful literature review of quantum field theory textbooks.
Some Classic Quantum Field Theory Courses
The late Sidney Coleman taught the quantum field theory course at Harvard for many years, influencing a generation of physicists in the way they view and teach QFT. Below you can find the pdf files of handwritten lecture notes for Coleman's course (transcribed by Brian Hill). The notes come in two large files, each around 6.5 Mb.
Another, older legendary QFT course was given in 1951 by Freeman Dyson. The notes are still relevant, and can be found here.