Manybody physicsAlex Tsyplyatyev, WS 2023/2024Lectures: 4 hours per week, on Wednesdays 14:0016:00 and on Fridays 12:0014:00 Room: Phys 01.114 (Wednesdays and Fridays) First lecture: 18.10.2023 Last lecture: 09.02.2024 (29 twohour lectures in total, 2 weeks of Christmas vacation 22.12.2023  05.01.2024) Tutorials: 2 hours every second week on Fridays 10:0012:00 Room: Phys 01.114 Tutor: Mr. Dmytro Tarasevich/Mr. Renan Hirayama First tutorial: 03.11.2023 (7 weeks of tutorials in total, dates are 03.11, 17.11, 01.12, 15.12, 12.01, 26.01, 09.02) This manybody course builds on top of the traditional bachelor courses in theoretical physics and is aimed at all students starting from the 7th semester. It introduces the foundations of the quantum field theory methods needed for describing systems consisting of many interacting particles in the solidstate physics. The prerequisites for this course are all of the bachelor theory courses (VHT15). Knowledge of the advanced quantum mechanics is advantageous but is not strictly necessary, its relevant parts will be briefly introduced at the beginning of this course. Announcements The tutorial classes start on Friday the 3rd of November. Lecture notes Week
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Complete lecture notesProblem sheets
 Ladder operators, Their matrix representation, Conservation of particle number.
 Green function of an interacting system, Fourier transform of the Theta function, Spectral function.
 Time evolution operator in the interaction picture, Infinite sums via the residue theorem, SokhotskyPlemelj formula.
 Spectral representation of the retarded Green's function, Density of states of a manybody system, Finitetemperature Green function of a noninteracting system.
 Wick's theorem, Second order Feynman diagrams
 Selfenergy of the Hubbard Model in perturbation theory
 Divergent perturbation theory in one dimension, Spectral function of Luttinger liquid
Master solutions Ladder operators, Their matrix representation, Conservation of particle number.
 Green function of an interacting system, Fourier transform of the Theta function, Spectral function.
 Time evolution operator in the interaction picture, Infinite sums via the residue theorem, SokhotskyPlemelj formula.
 Spectral representation of the retarded Green's function, Density of states of a manybody system, Finitetemperature Green function of a noninteracting system.
 Wick's theorem, Second order Feynman diagrams
 Selfenergy of the Hubbard model in perturbation theory
 Divergent perturbation theory in one dimension, Spectral function of Luttinger liquid
Content of the course  Introduction: the manybody problem in physics
 Second quantisation
 Common manybody models
 Green functions at T=0 and T>0
 Landau's Fermi liquid in D>1
 Grand potential in the diagrammatic language
 Random phase approximation
 Ladder approximation
 Bosonisation technique
 Luttinger liquid in D=1
Literature  A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics, Dover, New York, 1975. (main book for Green functions)
 T. Giamarchi, Quantum physics in one dimension, Clarendon press, Oxford, 2010. (main book for Luttinger liquid)
 R. D. Mattuck, A guide to Feynman diagrams in the manybody problem, Dover, Toronto, 1992.
 G. D. Mahan, Many particle physics, Kluwer, New York, 2000.
