# QM2: Quantum field theory

Module title: Quantum field theory (QM2)

Module convenor: Sam Carr (Birmingham)

* Update (April 2009): The remaining lectures will be on Tuesdays at 1.00-3.00. The schedule is the following:*

Tuesday 28th April: QM2a Lecture 9

Tuesday 5th May: No Lecture (I'm away)

Tuesday 12th May: QM2a Lecture 10

Tuesday 19th May: QM2b Lecture 1

Tuesday 26th May: QM2b Lecture 2

Tuesday 2nd June: QM2b Lecture 3

Tuesday 9th June: QM2b Lecture 4

Tuesday 16th June: QM2b Lecture 5

*Please let me know ASAP if there is a problem with any of these dates or times.
*

The aim of this module is to progress from some of the concepts learned in the QM1 module and learn techniques commonly used to solve interacting many-body problems. This module will focus on Green function techniques and diagrammatic expansions, and will aim not only to give the technical information necessary to carry out such calculations but also through many examples demonstrate many of the physical concepts involved in interacting electron systems.

Prerequisites:

- A working knowledge of second quantisation, as exposed in QM1
- Ability to do simple contour integration, in almost all cases involving only simple poles
- Some fluency with the techniques of Fourier series and Fourier transforms

The course is a double-module, so will consist of 10 lectures of 2 hours each, on Tuesday's from 1.00-3.00pm. It will begin on Tuesday 6th January, 2009.

Syllabus:

- Elemantary excitations and the free electron gas
- Greens functions
- Wicks theorem, S-matrix, diagrams at zero temperature
- Dyson series, self-energy, example: Hartree-Fock theory
- Examples: RPA, Thomas-Fermi screening, Plasmons, Fermi-liquid theory
- Examples: Diagrams for disorder: single impurity, quenched disorder
- Examples: Phonons and electron-phonon coupling, BCS theory of superconductivity
- Fluctuation-dissipation theorem, Lehmann (spectral) representation, Kubo formulae
- Wick rotation, Matsubara Green's functions, and diagrams at finite temperature
- Some examples at finite temperature