TVI/TMP-TA3: Condensed Matter Many-Body Physics and Field Theory I – Overview

!!!  NEW !!!  registration per LSF is compulsory for this course. It is likely that teaching (at least in the first weeks) will be per video conferencing (Zoom). Invitations to the meeting (lectures and tutorials) will be sent out via the LSF system, hence the mandatory registration in LSF.

We will migrate to Moodle for the lecture notes and exercise sheets

Tutors

Dr. Lukas Rammelmüller

Announcements

first lecture: Tue, April 21

first exercise: Tue, May 5

Details

Scope:  this course is designed 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 B101
               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.

Topics:

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

Credits/Exam:

9 ETCS credits. 

Office Hours:

TBA