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.
These lecture notes can also be viewed in HTML format which may be more accessible for screen readers.
“The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.”
Sidney Coleman
Preliminaries
Classical Field Theory
Table of Contents; Introduction; Lagrangian Field Theory; Lorentz Invariance; Noether's Theorem and Conserved Currents; Hamiltonian Field Theory.
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
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
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.
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
Quantum Electrodynamics
Gauge Invariance; Quantization; Inclusion of Matter -- QED; Lorentz Invariant Propagators; Feynman Rules; QED Processes.
I originally gave these lectures at the University of Cambridge, but later repeated them at the Perimeter Institute, where they were filmed.
Lecture 1
Introductory remarks on quantum field theory and classical field theory, roughly covering pages 1-10 of the printed notes.
Lecture 2
Noether's theorem and the energy momentum tensor: pages 11-17 of the printed notes.
Lecture 3
A few last comments on classical field theory. The beginning of canonical quantization for the free scalar field. Roughly pages 18-24 of the printed notes.
Lecture 4
More on canonical quantization, including normal ordering, the vacuum and the interpretation of particles. Pages 25-33.
Lecture 5
Yet more canonical quantization, including the Heisenberg picture and causality. Pages 34-38.
Lecture 6
Propagators. The beginnings of interactions. Pages 38-41 and 47-50.
Lecture 7
Interactions. Dysons formula and a first look at scattering. Pages 50-55.
Lecture 8
Wick's theorem, Feynman diagrams and examples of scattering amplitudes. Pages 56-62.
Lecture 9
Finishing off scattering amplitudes. A look at the algebra of the Lorentz group. Roughly pages 62-69 and 81-84.
Lecture 10
The spinor representation of the Lorentz group. The Dirac equation. Pages 85-90.
Lecture 11
Solving the Dirac equation and a first look at quantization and statistics. Various bits from pages 90-108.
Lecture 12
Quantizing fermions. Scattering amplitudes. Pages 108-118.
Lecture 13
Quantum Electrodynamics. Gauge fixing. Quantization in Lorentz gauge. Pages 124-134.
Lecture 14
Coupling light and matter. Feynman rules. Scattering amplitudes. Pages 135-The End.