## Field Theory in Condensed Matter

### Prof. J. Cardy - Hilary Term 2012

This 15-lecture course will cover several important applications of field
theoretic methods to condensed matter physics, but, despite its title, it should also be of interest to particle theorists.

It will begin with an extended account of renormalisation, and the renormalisation group, in scalar (phi^4) field theories.
This is essential background material for particle theorists wishing to understand these ideas in more complicated quantum field theories with spin and gauge symmetries.
Moreover it is of direct relevance for applications to critical phenomena, where the lectures
will make contact with the approach to the RG described in last term's lectures on Advanced Statistical Physics given by Professor Golestanian.

After this, a number of options are possible, depending on the interests of the students, for example: field theories for dynamical and quantum critical behaviour; 2d conformal field theory; integrable
field theories in 2d.

Previous exposure
to the path
integral approach to quantum field theory, and Feynman diagrams, will
be assumed, but there will be some revision of these ideas at the beginning
of the course if necessary.

The lectures will take place (with a few exceptions) in the Fisher Room on Thursdays at 12.00 and Fridays at 11.00.

### Outline

- Renormalisation
- Analysis of divergences and regularisation
- Mass, field and coupling constant renormalisation
- Example of a one-loop computation in scattering theory

- Renormalisation Group in Field Theory
- Callan-Symanzik equation
- RG flows
- One- and two-loop computation in phi^4 theory
- Composite operators
- Application to critical phenomena
- Large N in the O(N) model

- Possible further topics
- Dynamic critical behaviour at finite temperature
- Quantum critical behaviour
- 2d conformal field theories
- Integrable massive 2d field theories

Return to my home page for more details.

Last updated 3 January 2012.