# Part III - Quantum Field Theory

## Lectured by B. Allanach, Michaelmas 2016

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

This is an HTML version of the notes, generated using some horribly-written scripts and pdf2htmlEX. These are not guaranteed to display well, but do let me know if something is broken. Note however that I cannot help you if your browser does not support standard HTML features (eg. this part is known not to work well with w3m). You can either view all sections in a single page (Full version), or access individual sections below. If you want to download a pdf, head to the Notes page.

# Contents

- V Full version
- 0 Introduction
- 1 Classical field theory
- 1.1 Classical fields
- 1.2 Lorentz invariance
- 1.3 Symmetries and Noether's theorem for field theories
- 1.4 Hamiltonian mechanics
- 2 Free field theory
- 2.1 Review of simple harmonic oscillator
- 2.2 The quantum field
- 2.3 Real scalar fields
- 2.4 Complex scalar fields
- 2.5 The Heisenberg picture
- 2.6 Propagators
- 3 Interacting fields
- 3.1 Interaction Lagrangians
- 3.2 Interaction picture
- 3.3 Wick's theorem
- 3.4 Feynman diagrams
- 3.5 Amplitudes
- 3.6 Correlation functions and vacuum bubbles
- 4 Spinors
- 4.1 The Lorentz group and the Lorentz algebra
- 4.2 The Clifford algebra and the spin representation
- 4.3 Properties of the spin representation
- 4.4 The Dirac equation
- 4.5 Chiral/Weyl spinors and γ
^{5} - 4.6 Parity operator
- 4.7 Solutions to Dirac's equation
- 4.8 Symmetries and currents
- 5 Quantizing the Dirac field
- 6 Quantum electrodynamics