Field theoretical methods in solid state physics: Many body systems, exact and approximate methods. Green's functions  propagators. Definitions, properties. Perturbation method, Feynman diagrams. Vacuum fluctuations, connected and disconnected diagrams. Linked Cluster Theorem. Particle selfenergy, Dyson equation. Quasiparticle  definition and properties. Ground state energy: Coulomb (Hartree) and exchange (Fock) energies, correlation energy; Equation of motion for the Green's function, solution methods (Hartree, HartreeFock); Boson Green's functions; Fermionboson interaction; Polaron, renormalization of particle mass and energy
Linear response theory: Correlation functions and the differential cross section. Dynamical and static structure factors; Neutron and xray scattering in crystals: differential cross section, elastic scattering, DebyeWaller factor, phonon emission and absorption; Response functions ; Kubo formula, spectral representation; Properties of response functions, connection with correlation functions; Free fermion response function (Lindhard);Static and dynamic limits, Kohn anomaly and Friedel oscillations;Boson response function;Currentcurrent response function. Conductivity. Optical properties.
Collective phenomena in the Coulomb gas: Dynamically screened Coulomb interaction. Random Phase Approximation (RPA); Excitation spectrum, plasmons in the electron gas. Landau damping; Dynamical and static longwavelength limits. ThomasFermi screening; Connection with the dielectric function; GW approximation, ground state energy
Electron states in condensed matter : Localized state spectra; Nonperturbative calculation, cumulant expansion, Independent Boson Model (IBM); Properties of the spectra: ground state energy shift, satellites, sum rules, Koopmans theorem; Adiabatic and sudden transitions, effects on relaxation and screening; Examples: electronphonon and electron electron interaction, discrete and continuous excitations; Electronic state decay, irreversibility, FanoAnderson model; Delocalized state spectra; Radiation absorption spectra
Density functional theory: KohnHohenberg theorem, ground state energy as the density functional; Selfconsistent KohnSham equations; Local density approximation (LDA), Approximations for the exchange and correlation energy; Examples, discussion of the results
Density matrices: Definitions and properties. Natural orbitals; HartreeFock approximation; Free fermions  Fermi hole; Pair distribution function and the static structure factor

 A.P.Abrikosov, J.I.Gorkov, I.E. Dyaloshinskii, Methods of Quantum Field Theory in Statistical Physics, (new ed.), Dover 1976
 A.L.FetterJ.D.Walecka: Quantum Theory of ManyParticle Systems, McGraw Hill, New York, 2003
 M. Šunjić: Kvantna fizika mnoštva čestica, (Školska knjiga, Zagreb, 2002)
 G.D.Mahan: ManyParticle Physics, Plenum, 1990
