**Winter semester, 2012/13. Hours: Wednesdays, 09:10-12:00. **

- Many-body theory - principles and methodology

- Overview of methods of many-body condensed matter physics.

- Second Quantization

- Effective Hamiltonians - Spin Chains

- The Hartree Fock Approximation and the Ground-state energy of an
interacting electron gas -

- Density functional theory

- Formulation of perturbation theory - Green functions and their
relation to physical observables

- Ground-state energy of an interacting electron gas -
beyond the Hartree-Fock approximation

- Response of an interacting electron gas to an external field

- The concept of quasi-particles and Fermi-liquid theory

- Fermi-liquid and the renormalization group.

- Non-Fermi-Liquid behavior - an interacting electron gas in one
dimension. The bosonization approach to a Luttinger liquid.

- Methods and concepts of many-body condensed matter physics -
revisited

**Spring semester, 2010. Hours: Wednesdays, 17:10-21:00.**

- Matsubara Green functions
- Keldysh Green Functions
- The Kondo problem:

The Kondo model and perturbation theory

Anderson's poor man scaling

Nosieres'Fermi liquid description and the two-channel model

The Anderson model and the Schrieffer-Wolf transformation

Perturbation theory for the Anderson model

Slave boson mean-field theory

Books:

- Green's Function in Solid State Physics, Doniach & Sondheimer
- Many-Particle Physics, Mahan
- Many-Particle Theory, Gross, Runge and Heinonen
- Quantum Liquids, Pines and Nosieres
- Condensed Matter Field Theory, Altland and Simons
- Many Body Quantum Theory in Condensed Matter Physics, Bruus and Flensberg
- Quantum Theory of the Electron Liquid. Giuliani and Vignale

On-line sources

**Homework Assignments:**

**first semester**

- Exercise #1
- Exercise #2
- Exercise #3
- Exercise #4
- Exercise #5
- Exercise #6
- Exercise #7
- Exercise #8
- Exercise #9