Quantum fields for experimental condensed matter physics

Tom Lancaster (t.lancaster1_at_physics.ox.ac.uk)

This is a 10 lecture graduate course intended primarily for new students of experimental physics in Oxford's Condensed Matter Physics subdepartment, although all are welcome to come to the lectures.

What and when

The course is intended to be an unfrightening guide to some of the quantum mechanics used in modern Condensed Matter Physics. The word "experimental" in the title means that the emphasis on the course will be on understanding concepts and we'll avoid many of the detailed calculations needed by those wanting to work in this area professionally.

The lectures will run in Michalemas 2011 as follows:

Weeks 2-3 and weeks 5-7, Mondays and Tuesdays, 2pm-3pm, venue: Fisher Room, Dennis Wilkinson Building.

List of topics

The structure will be fairly informal, but my aim is to cover the following topics in varying levels of detail:

Second quantization and the coupled oscillator problem
Occupation number representation
Time evolution and the need for quantum fields
Lagrangians and canonical quantization
Examples of second quantization in many body physics
Some aspects of the many body problem
Perturbation theory
Path integral methods
The renormalization group

Notes and Problem sets

A note on conventions and useful maths is available: conventions.pdf.

My (messy and handwritten) notes will be made available here. I've not yet corrected them from last year, so beware. You are recommended to take your own notes during the lectures! (I'd be grateful if people can let me know when they find errors.)

A problem set for the course is available: problems.pdf.

Here's the feedback form to tell me what you thought of the course: qftfeedback.pdf.

Reading list

Books on QFT tend to be difficult and all emphasise different aspects of the subject. The following are a selection of the clearer books with parts I've found useful in writing the lectures.

Elements of advanced quantum theory, J.M. Ziman
Probably the best text for this course in terms of length and the level of the material. Inevitably rather old fashioned now.
Condensed matter field theory, A. Altland and B Simons
Good all-round guide to the theory with applications in Condensed Matter, but possibly quite tough for beginners. Probably the best book to buy for the future, if you insist on buying a book at this stage.
Quantum field theory in a nutshell, A. Zee
One of the gentler introductions to the general theory. It's entertaining, but moves very swiftly.
Gauge theories in particle physics, I.J.R. Aitchison and A.J.G. Hey
Not a Condensed Matter book, but it does contain a very clear introduction to quantum field theory.
A guide to Feynman diagrams in the many body problem, R.D Mattuck
Excellent, intuitive guide to perturbation theory in the first few chapters. Rather tortuous structure.

These pages were last updated on 19/09/2011.