Quantum Many-Body Physics

Lecturer: Sergej Moroz 
Teaching Assistants: Claudio Benzoni, Umberto Borla

Lectures: Mon&Wed 10:15-11:45, seminar room 3344 
Tutorials: Mon 8:30-10:00, Thu 16:15-17:45, Handbibliothek- seminar room 3343

This course provides an introduction into quantum many-body physics. We will cover basic quantum many-body methods and their application to various many-body problems of condensed matter theory, such as Fermi and Luttinger liquids, superfluids and superconductors and quantum Hall fluids. This course will provide students with a basic knowledge for starting independent research in quantum condensed matter physics. The practical classes will supplement the lectures with regular tutorials and problem sets.


Introduction into quantum many-body problem: emergence and collective behavior [pdf], quantum fields, second quantization [pdf], quantum statistical physics from second quantization [pdf]

Path integral formulation of quantum field theory: single-particle quantum mechanics from the path integral, partition function as a functional integral [pdf], coherent states and functional integrals [pdf]

Linear response theory: response functions, classical Drude formula for conductivity, calculation of electromagnetic linear response in quantum physics, f-sum rule [pdf]

Fermi liquid theory: Fermi liquid ground state, quasiparticles and their stability, collective modes, Landau damping, non-Fermi liquids [pdf], Green's function and self-energy [pdf]

Luttinger liquids: peculiarities of physics in one dimension, Tomonaga-Luttinger model, basic of bosonization [pdf], correlation functions [pdf]

Superfluids and superconductors: physical properties of superfluids and superconductors, BCS theory [pdfpdf], spontaneous symmetry breaking and phase stiffness [pdf], vortices [pdf], Higgs mechanism in superconductors [pdf], boson-vortex duality in two dimensions [pdf], Berezinskii-Kosterlitz-Thouless transition [pdf], chiral superfluids and superconductors [pdf]


Problem set 1 [pdf]
Problem set 2 [pdf]
Problem set 3 [pdf]
Problem set 4 [pdf]
Problem set 5 [pdf]
Probelm set 6 [pdf]




P. Coleman, Introduction to Many-Body Physics
A. Altland & B. Simons, Condensed Matter Field Theory 
T. Giamachi, Quantum Physics in One Dimension 
E. Fradkin, Field Theories of Condensed Matter Physics 
X.-G. Wen, Quantum Field Theory of Many-Body Systems