## 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.

**Outline:**

**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 [pdf, pdf], 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]

**Tutorials:**

Problem set 1 [pdf]

Problem set 2 [pdf]

Problem set 3 [pdf]

Problem set 4 [pdf]

Problem set 5 [pdf]

Probelm set 6 [pdf]

**Literature:**

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