QM2: Quantum field theory

Module title: Quantum field theory (QM2)

Module convenor: Sam Carr (Birmingham)

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

Probably beginning Thursday 24th January, but to be confirmed shortly. The course will be given in 10 lectures of 2 hours each.

Syllabus: (Tentative)

  • 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

New information...
Last term, we managed to have 6 out of the 10 lectures. I intend to give the remaining 4 lectures this term, beginning Thursday 1st May, same time as before (11.00am). If this time is not convenient for anybody, e-mail me (carrst@th.ph.bham.ac.uk) as soon as possible so we can arrange a new schedule.

Update, 21st May 2008...
We've finished 10 lectures now, but we've decided to continue informally for the forseeable future. Lectures are now 11.00am on Wednesdays. Subjects I hope to cover are Finite-T Green's functions, phonons, weak localization, and maybe if there is time, the path integral approach.

The problem sheet is now available for download from this webpage. It is based on material from the first nine lectures (so no finite-T stuff). Please get answers to me by the end of June if you want to get credit for this module.

Duration: 
2hrs
Starts: 
24/01/2008 - 11:00