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Many-body physics

Alex Tsyplyatyev, SS 2019

Lectures: 4 hours per week, Wednesdays 14:00-16:00 and Fridays 10:00-12:00
Room: Phys __.102 (Wednesdays) and Phys 02.120 (Fridays)
First lecture: 17.04.2019
Last lecture: 19.07.2019 (13 weeks of lectures in total, 19.04 and 01.05 are public holidays)

Tutorials: 2 hours every second week on Thursdays 12:00-14:00
Room: Phys 01.114
Tutor: Mr. Jan Krieg
First tutorial: 25.04.2019 (7 weeks of tutorials in total, dates are 25.04, 09.05, 23.05, 06.06, 13.06, 27.06, 11.07)

This many-body course builds on top of the traditional bachelor courses in theoretical physics and is aimed at all students starting from the 7th semester. It introduces the foundations of the quantum field theory methods needed for describing systems consisting of many interacting particles in the solid-state physics. The prerequisites for this course are all of the bachelor theory courses (VHT1-5). Knowledge of the advanced quantum mechanics is advantageous but is not strictly necessary, its relevant parts will be briefly introduced at the beginning of this course.

Announcements

The tutorial classes start on Thursday the 25th of April.

The oral exam takes place on Wednesday September 4th in the room 02.120 at 11:00.

Lecture notes

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Complete lecture notes

Problem sheets

  1. Ladder operators for fermions, Conservation of the particle number
  2. Equation of motion for Green function, Fourier transform of theta function, Spectral function
  3. Time evolution operator, Infinite sums via residue theorem, Sokhotsky-Plemelj formula
  4. Spectral representation of retarded Green function, Density of states, Green function of noninteracting system at finite T
  5. Wick's theorem in thermodynamics, Second order Feynman diagrams for grand canonical potential
  6. Self-energy of the Hubbard model
  7. Divergence of perturbation theory in interaction in 1D, Spectral function of Luttinger liquid

Content of the course

  1. Introduction: the many-body problem in physics
  2. Second quantisation
  3. Common many-body models
  4. Green functions at T=0 and T>0
  5. Landau's Fermi liquid in D>1
  6. Grand potential in the diagrammatic language
  7. Random phase approximation
  8. Ladder approximation
  9. Bosonisation technique
  10. Luttinger liquid in D=1
Literature
  • A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Dover, New York, 1975. (main book for Green functions)
  • T. Giamarchi, Quantum physics in one dimension, Clarendon press, Oxford, 2010. (main book for Luttinger liquid)
  • R. D. Mattuck, A guide to Feynman diagrams in the many-body problem, Dover, Toronto, 1992.
  • G. D. Mahan, Many particle physics, Kluwer, New York, 2000.