David Tong: Quantum Field Theory

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.

PDF       Videos       HTML


  • 0. Preliminaries:   Postscript    PDF
  • 1. Classical Field Theory:   Postscript    PDF
    Table of Contents; Introduction; Lagrangian Field Theory; Lorentz Invariance; Noether's Theorem and Conserved Currents; Hamiltonian Field Theory.
  • 2. Canonical Quantization:   Postscript    PDF
    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:   Postscript    PDF
    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:   Postscript    PDF
    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:   Postscript    PDF
    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:   Postscript    PDF
    Gauge Invariance; Quantization; Inclusion of Matter -- QED; Lorentz Invariant Propagators; Feynman Rules; QED Processes.

Problem Sheets

  • 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

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.

Part 1      Part 2

These notes were subsequently latexed and posted on the arXiv. The original videos of Coleman's course from the mid 1970's are also available here.

Another, older legendary QFT course was given in 1951 by Freeman Dyson. The notes are still relevant, and can be found here.