# Quantum fields for experimental condensed matter physics

## Tom Lancaster (tom.lancaster_at_durham.ac.uk)

This is a 10 lecture graduate course intended primarily for new students of experimental condensed matter physics.

### What’s involved

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.

### 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.