Quantum Theory of Solids

Field quantization. Occupation number representation for nonrelativistic fermionic and bosonic many-particle systems. Interacting electron gas. Green's functions. Many-particle perturbation theory and Feynman diagrams. Lattice models for fermions and spins. The Hubbard model and the Heisenberg model. Spin-wave theory of ferro- and antiferromagnets. Electron-phonon coupling. The Cooper problem and the BCS theory of superconductivity.

The students will obtain knowledge of key examples of field theories and lattice models for systems of interacting fermions, bosons, and spins, and learn to use relevant theoretical concepts and methods to analyze various aspects of these models. More specifically, the students will:

• master the use of creation and annihilation operators for fermion and boson systems
• master Fourier and Bogoliubov transformations for diagonalization of quadratic Hamiltonians
• be introduced to many-particle Green functions and how these are related to various quantities of interest
• get an introduction to many-particle perturbation theory, including Feynman diagrams
• acquire knowledge about various other methods, e.g. spin wave theory
• learn about key concepts, including quasiparticles, order parameters, and (broken) symmetries.

Lectures and voluntary homework problems. The course will be given in English if students in the international master program in physics are attending the course. Expected workload in the course is 225 hours.

The course has joint lectures with TFY4210.