Despite its rather general title, this course will in fact be an introduction to the use of field theory methods in understanding dynamical behaviour in the vicinity of a phase transition, both close to and far from equilibrium, in both the classical and quantum regimes.

However, a knowledge of the field theory approach to equilibrium
critical behaviour (renormalisation group, epsilon expansion) will
not be assumed, and will be covered in the first few lectures. It
will be assumed that the audience is familiar with the path integral
formulation of scalar field theory and Feynman diagrams as taught,
for example, in the
Michaelmas term QFT course, as well as the basic phenomenology of
critical behaviour as discussed in my book
*Scaling and Renormalization in Statistical
Physics*
and in the
course
I taught based on this in Hilary Term 2005.

Lectures will be on Tuesdays
and Fridays at 11 am in the Fisher
Room, Denys Wilkinson Building. ** However there will be no lectures on
the following dates:**

- Fri. May 5 (week 2)
- Tues. May 8 (week 3)
- Fri. May 26 (week 5)
- Fri. June 2 (week 6)

Topics to be covered may include, depending on time and audience interest (there won't be time to cover all these!):

- Equilibrium critical behaviour
- Field theory (Landau-Ginzburg-Wilson) description of equilibrium phase transitions
- Feynman diagrams, renormalisation, and the renormalisation group (RG)
- Critical exponents and the epsilon-expansion

- Critical dynamics close to equilibrium
- Detailed balance and fluctuation-dissipation relation
- Time-dependent Landau-Ginzburg equations
- Gaussian approximation and mode coupling theory
- Dynamic perturbation theory and Feynman diagrams
- RG analysis and dynamic scaling
- The zoo of models

- Critical dynamics far from equilibrium
- Reaction-diffusion systems and the Doi-Peliti formalism
- Driven diffusive systems, KPZ equation

- Quantum critical dynamics
- Schwinger-Keldysh formalism
- Caldeira-Leggett formalism

- Lecture notes I: field theory RG for static equilibrium critical behaviour (scanned pdf file).
- Lecture notes II: dynamical and non-equilibrium classical systems.
- Short list of further reading.