"The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction."
-- Sidney Coleman.
David Tong: Lectures on Quantum Field Theory
These notes are based on an introductory course on quantum field theory, given to Part III (i.e. masters level) students in the fall of 2006 and 2007. They were also given at the Perimeter Institute PSI programme in 2009. The full set of lecture notes can be downloaded here. They come in at about 150 pages. Individual sections can be downloaded below. Please email me any typos or comments. Last updated June 2008.
Videos of the lectures given at the Perimeter Institute can be found here.
Content : Quantum Field Theory Lecture Notes
- 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
- Quantum Field Theory by Michael Luke.
- Fields by Warren Siegel.
- General Field Theory by Eduardo Fradkin.
- Quantum Condensed Matter Physics by Chetan Nayak.
- Quantum Condensed Matter Field Theory by Ben Simons
- Errata for the book by Peskin and Schroeder
Philip Tanedo, a student from last year's course, 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.
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.