Introduction to Quantum Fields: collective quantum fields, harmonic oscillator-zero dimensional field theory, collective modes-phonon, the thermodynamic limit, the continuum limit; Bosons and Fermions: commutation and anti-commutation algebras, field operators, field operators as creation and annihilation operators, interaction, equivalence between many-body Schrodinger equation, identical particles in thermal equilibrium, Jordan-Wigner transformation, the Hubbard model, non-interacting particles in thermal equilibrium; Green’s Functions: driven harmonic oscillators, interaction, Wick’s theorem, generating functional, Green’s functions for bosons and fermions, Gell-Man-Low theorem, generating functional for free fermions, spectral representation; Landau Fermi-liquid Theory: quasiparticle concept, neutral Fermi liquid, Landau parameters, the equilibrium distribution of
quasiparticles, a renormalization of paramagnetism, mass renormalization, quasiparticle scattering amplitudes, Landau-Silin theory, inelastic quasiparticle scattering, the microscopic basis of Fermi-liquid theory; Zerotemperature Feynman Diagrams: the path integral-general formalism, construction of path integral, construction of many-body path integral, field integral for the quantum partition function, Feynman diagrams, symmetry factors, Feynman rules in momentum space, Hartree-Fock energy, exchange-correlation, an electron in scattering potential, response functions; Finite-temperature many-body physics: imaginary time, periodicity and antiperiodicity, Matsubara representation, the contour integral method, generating function, and Wick’s theorem, Feynman diagram, linked-cluster theorem, Hartree-Fock at finite temperature, an electron in disordered potential, electron-phonon interaction, mass renormalization, Migdal’s theorem; Linear Response Theory: fluctuation-dissipation theorem for a classical harmonic oscillator, quantum mechanical response function, spectral decomposition-correlation function, retarded response function, quantum fluctuation-dissipation theorem, calculation of response function, spectroscopy, Kramers-Kronig relation, the Kubo formula, Drude conductivity, electron diffusion, Anderson localization.