Fakultät für Physik




TVI/TMP-TA3: Many-Body Physics – Overview

Condensed Matter quantum many-body systems and Field Theory I


About the lecture

Time and place

Tue, 8.15 - 9.45 am, C111
Thu, 8.15 - 9.45 am, A348


Dr. Ke Liu


first lecture: Tue, April 23

first exercise: Tue, May 7


On Tue, July 23 : no theory class at 8.15am, exercise class takes place as usual.

On Thu, July 25 : Question and Answers Session at 8.15am



Scope: after discussing with my colleagues this course is redesigned to include both standard many-body techniques and field theory and should hence be called "Condensed Matter Quantum Many-Body Systems and Field Theories I" (CM-QMB-FT-1) It should be the workhorse for future theorists in the many-body condensed matter area. The course "Field Theory in condensed matter physics", offered in the winter term, will be seen as the successor to this course and should hence be seen as a  CM-QMB-FT-2.

Lectures: Tuesdays 08:15 - 9:45 in room C111
Thursdays 08:15 - 9:45 in room A348

Tutorials: Tuesdays 12:15 - 13:45 in room A249

Prerequisites: Quantum Mechanics, Statistical Physics, Solid State Theory

Aim: The aim of this course is to learn basic methods of modern many-body theory and to apply them to various problems in condensed matter physics. At the end of the course students should be familiar with the tools to follow current research topics and be able to start independent research.


  1. Second quantization & applications
    (Hubbard- and Heisenberg models, SDW mean-field theory, weakly interacting bosons, Hartree-Fock, BCS wavefunction)
  2. Functional integrals
    (Path-integral representation of the partition function, Grassmann variables, coherent states, functional integrals)
  3. Diagrammatic perturbation theory
    (analytical properties of Green functions, spectral functions, Kramers-Kronig relations, Matsubara formalism, Wick theorem, Feynman diagrams, Dyson equation)
  4. Linear response and Kubo formula
    (analytic properties of correlation functions, fluctuation-disspiation theorem, (spin) susceptibility, dielectric function)
  5. Hubbard-Stratonovich transformation, collective modes
  6. The electron gas (physics of screening and plasmons, RPA)
  7. BCS theory of superconductivity (pairing mechanism, gap equation, ladder summation)
  8. Fermi liquid theory

Useful Literature:

P. Coleman: "Introduction to Many-Body Physics"
A. Altland, B. Simons: "Condensed Matter Field Theory"
H. Bruus, K. Flensberg: "Many-Body Quantum Theory in Condensed Matter Physics: An Introduction"
J.W. Negele, H. Orland: "Quantum Many-Particle Systems"
G.D. Mahan: "Many-particle physics"
A. Auerbach: "Interacting Electrons and Quantum Magnetism"

additional literature on special topics will be announced in the lecture


9 ETCS credits. Exam: for the results, see the exam tab

Office Hours:


Verantwortlich für den Inhalt: Lode Pollet