Theoretische und Mathematische Physik

This lecture, Condensed Matter Many-Body Physics & Field Theory II, explores advanced concepts at the intersection of quantum field theory and condensed matter physics. We begin with a recap of fundamental tools, including the path-integral formulation, Feynman diagrams, and the classification of many-body states such as Bose–Einstein condensates, Fermi liquids, and superconductors. From there, we turn to charged Fermi liquids, examining screening, plasma modes, and the Bardeen–Pines interaction. A central focus will be linear response theory, with emphasis on response functions, the fluctuation–dissipation theorem, transport phenomena, and the Kubo formalism. Building on this foundation, we study BCS theory and charged superfluids, highlighting path-integral approaches, mean-field methods, and the Ginzburg–Landau description of superconductivity, including the Meissner effect and Anderson–Higgs mechanism. The course then transitions to quantum magnetism, starting with the Fermi–Hubbard model, its mean-field phases, and the Heisenberg model in the strong coupling limit. We will also explore effective field-theory descriptions such as the non-linear sigma model, topological terms, and resonating valence bond states in frustrated magnets. Next, we investigate topological phases of matter and quantum Hall physics, covering topological invariants, Berry phases, edge states, fractionalization, and Chern–Simons field theories. Finally, we turn to strongly correlated electron systems, introducing Kondo physics, heavy fermion materials, and exotic Fermi liquids, before concluding with lattice gauge theories in condensed matter and the doped Hubbard model. Throughout, the lectures emphasize both formal techniques and their physical consequences, preparing students to engage with current research questions in modern condensed matter physics.