Methods of QFT in Condensed Matter

Time and Location of Lectures:

  • Room A449, Theresienstrasse 37.

    NOTE: Time/venue of lectures can be changed!

    Guest Lecturers:

  • Igor Yurkevich (University of Birmingham) - Lectures No.1-7
  • Kurt Schoenhammer (University of Goettingen) - Lectures No.8-12
  • Herbert Schoeller (Physikzentrum der RWTH Aachen) - Lectures No. 19-23

    Local Coordinators and Lecturers:

  • Jan von Delft
  • Oleg Yevtushenko (Lectures No.13-18)

    Outline of lectures 1-7

  • Path integral: classical stochastic problems, quantum mechanics in 1st quantization.
  • Gaussian integrals. Wick's theorem.
  • Quantum Field Theory: quantization of elastic string, path integral representation.
  • Second quantization. Fock space, statistics, coherent states. Functional integral representation for bosons an fermions.
  • One dimensional problems: chiral fermions and bosons.
  • Luttinger Liquid.

    Lecture Notes

  • Lectures 1 and 2
  • Lectures 3 and 4
  • Lecture 5
  • Lectures 6 and 7

    Topic of lectures 8-12: Introduction to the functional renormalization group

    Lecture Notes

  • Introduction to fRG - Part I
  • Introduction to fRG - Part II

    Topic of lectures 13-18: Introduction to the SuSy-FT for disordered systems

    Lecturer: Oleg Yevtushenko

    Schedule

  • March: 8, 13, 15, 20 - at 10:15, room A449
  • March: 21 (SuSy-5 & SuSy-6) - at 14:15, room A449

    Lecture SuSy-1:

  • models of disordered systems;
  • Green's functions as functional integrals;
  • disorder averaging: ``the problem of denominator''.

    Lecture SuSy-2:

  • the supersymmetry trick;
  • Grassmann variables, supervectors, supermatrices, superintegrals;
  • from a random non-interacting model to the deterministic one with effective interactions.

    Lecture SuSy-3:

  • disorder averaged Green's functions;
  • disorder averaged DoS, ``semicircle''.

    Lectures SuSy-4:

  • mean field solution;
  • self-energy of disorder averaged Green's functions.

    Lectures SuSy-5,6:

  • disorder averaged correlation functions;
  • unitary vs. pseudounitary symmetry;
  • SuSy sigma-model;
  • 0d case.

    Recommended literature

  • K. Efetov, Supersymmetry in disorder and chaos (Cambridge University Press).

  • A.D. Mirlin, Statistics of energy levels and eigenfunctions in disordered and chaotic systems: Supersymmetry approach (arXiv:cond-mat/0006421v1).

  • F. Haake, Quantum signatures of chaos (Springer series in synergetics, vol.54).

    Topic of lectures 19-23: Real-time RG treatment of the Nonequilibrium Kondo Effect

    4 lectures by H. Schoeller in the week Tue. 29./05 - Fri. 1/06


    Last Updated: 19.04.2012