E. Hardy - C6: QFT

This is the homepage for the Hilary term 2026 part of the C6 option.

Lectures will be in-person according to the standard C6 schedule . Tutorial classes are in weeks 4,6,8 of Hilary term, with a final one in Trinity term.

The topics covered are:
1. Classical field theory

2. Symmetries of the action. Noether's theorem

3. Spontaneous symmetry breaking. Goldstone's theorem

4. Canonical quantization of fields

5. Interacting quantum fields

6. Feynman diagrams

7. Path integrals in quantum field theory

8. Examples of interacting quantum field theories

Lecture notes

The main lecture notes can be found here
A brief summary of some background material, mostly covering material from previous years but possibly in slightly different style, can be found at notes . A useful introductory question (not covered in tutorials but useful) is here . It would be helpful to review these before or early on in the course.
The introductory slides are here
A streamlined summary of the formalism leading to Feynman diagrams can be found here (this is basically the same as the main notes, but might be useful as an overview)
Recommended books (by Prof. Starinets): literature

Problem Sheets

Sheet 1
Sheet 2
Sheet 3
Sheet 4 (covered in an extra session in Trinity term)

Additional resources

Handwritten lecture notes by Prof Andrei Starinets (lecturer in previous years) are available at http://www-thphys.physics.ox.ac.uk/people/AndreiStarinets/C6-MASTER/C6-starinets-2022-2023.html covering the same material but sometimes from a slightly different perspective.
Interesting discussion of the perturbative solution of classical field equations and the connection to Feynman diagrams: https://homepages.physik.uni-muenchen.de/%7Ehelling/classical_fields.pdf
The best discussion I know about of the meaning of "breaking" a gauge symmetry: http://theory.caltech.edu/~preskill/ph230/notes2000/230Lectures27-29-Page347-402.pdf
Lecture notes for an undergraduate QFT course, possibly useful to refresh your QM background https://physics.mcmaster.ca/~cburgess/Notes/QFTUGnotes.pdf
Extensive QFT lecture notes from Timo Weigand http://www.physics.umd.edu/grt/taj/624b/WeigandQFT.pdf (I think these are very useful)
Notes describing carefully how the non-relativistic limit of QFT occurs arxiv
Group theory course including (very useful) lecture notes by Prof A Lukas
Group theory notes by Prof Alessandro Tomasiello
QFT and other lecture notes by Prof John Cardy
A monumental QFT course by Prof Warren Siegel ("Fields")
Lectures on effective field theory by Prof Iain Stewart (MIT online course)