**Place and Time**: Wednesdays 15:15, Sala A. The course starts on 08.III.2017

**LECTURERS**: dr hab. Łukasz Cywiński prof. IF PAN and dr Piotr Szańkowski

contact: lcyw@ifpan.edu.pl and piotr.szankowski@ifpan.edu.pl

**BOOK**: The course will be mostly based on the book *Many-Body Quantum Theory in Condensed Matter Physics* by Henrik Bruus and Karsten Flensberg, with additional material based on *Condensed Matter Field Theory *by Alexander Altland and Ben Simons.

**LANGUAGE**: English

**AIMS/OBJECTIVES OF THE COURSE**:

This is the second part of the course on many-body quantum theory. The aim of these lectures is to show how the formalism of second quantization and Green’s function techniques (including the diagrammatic approaches) are used to tackle diverse physical problems (taken mostly from condensed matter physics).

**CRITERIA FOR ADMISSION**

The basic knowledge on quantum mechanics is expected of the participants of the course. Having taken the first part is going to be obviously helpful, but we believe that previous exposure to other lectures on second quantization and basics of Green’s function techniques in many-body physics should provide enough background. We are not going to assume that the participants will be perfectly fluent in the material covered in the first part. We will in fact revisit a few technical issues that were discussed during the first semester (the exact choice will depend on feedback from participants)

**TEACHING/LEARNING METHODS AND STRATEGIES:**

The course is organized in fifteen two hour long lectures. There will be home assignments, and they will be checked, graded, and discussed afterwards. The final course grade will be based on their grades.

**TOPICS WILL INCLUDE:**

- Model Hamiltonians in 2
^{nd}quantization: tight binding models, Heisenberg echange coupling, Hubbard model, Anderson’s model, Kondo’s Hamiltonian… - Mean field theory and symmetry breaking. Simple models of ferromagnetism
- Bosonic quasiparticles corresponding to collective excitations: phonons, spin waves (magnons). What are Goldstone modes? Holstein-Primakoff transformation.
- Conductivity from linear response.
- How to get something interesting out of Green’s functions without diagrammatics: equation of motion theory.
- Feynman diagrams and external potentials: conductivity and impurity scattering.