Quantum Field Theory

Introductory remarks on quantum field theory and classical field theory. Roughly covering pages 1-10 of the printed notes.

Noether's theorem and the energy momentum tensor. Pages 11-17 of the printed notes.

This lecture introduces the canonical quantization procedure for the free scalar field, building upon classical field theory and laying foundational concepts for advanced quantum field theory.

More on canonical quantization, including normal ordering, the vacuum and the interpretation of particles. Pages 25-33.

Heisenberg picture. Causality. Yet more canonical quantization, including the Heisenberg picture and causality. Pages 34-38.

This lecture from David Tong's Quantum Field Theory course at Perimeter Institute introduces the concept of propagators, detailing their derivation and role as Green's functions in describing particle interactions within quantum field theory, referencing specific sections of Tong's canonical lecture notes.

Interactions. Dyson's formula and a first look at scattering. Pages 50-55.

Wick's theorem, Feynman diagrams and examples of scattering amplitudes. Pages 56-62.

This lecture concludes the discussion on scattering amplitudes and delves into the intricate algebra of the Lorentz group, referencing pages 62-69 and 81-84 of the course notes.

This session introduces the spinor representation of the Lorentz group and rigorously derives the Dirac equation, covering material from pages 85-90.

The lecture focuses on methods for solving the Dirac equation and offers an initial exploration of quantization and statistics, drawing from pages 90-108.

This lecture details the process of quantizing fermions and extends the treatment to scattering amplitudes in the fermionic context, based on pages 108-118.

This session introduces Quantum Electrodynamics, explaining gauge fixing and the quantization of the electromagnetic field in Lorentz gauge, covering pages 124-134.

This lecture explores the coupling of light and matter, introduces Feynman rules, and revisits scattering amplitudes within this framework, concluding the course content.