Introduction to Quantum Theory Many Body Theory 1102-341

This course is an introduction for students, who are going to specialize both in experimental or theoretical physics, to a theoretical description of quantum systems composed of many interacting particles (fermions or bosons). We present basic and most important concepts of modern condensed matter physics by analyzing examples of many-particle wave functions: Hartree-Fock, BCS, Lauglin's and Gutzwiller's wave function and using simple perturbative methods. On a descriptive level we discuss notions of quasiparticles, spontaneous symmetry breaking, renormalization and emergent phenomena.
In a practical way the course introduces second quantization formalism, Fock spaces and some elements of density functional theory. The course should be very useful for students specializing in solid state physics, nuclear physics, quantum chemistry and biophysics. Future astrophysics and high-energy physics
students are also welcome.

Outline:
1. Introduction: particle statistics, symmetry of wave functions, particle number formalism (second quantization).
2. Crystals: order and collective bossing excitations (phonons) in harmonic approximation.
3. Weakly interacting bosonic gas: Bose-Einstein condensate and superfludity in mean-field approximation and Bogoliubov transformation.
4. Electron gas: Hartree-Fock approximation, screening, electrons as quasi-particles.
5. Superconductivity: BCS wave function, canonical transformation, Meissner effect, magnetic flux quantization.

Description by Jakub Tworzydło, January 2008
Amendments by Krzysztof Wohlfeld, September 2019