Syllabus
Nonrelativistic quantum dynamics, Fock space and second quantization; interacting fermions, bosons; model Hamiltonians of interacting systems in solid state theories: electron-electron and electron-phonon interaction.
Interaction representation, S-matrix, Green functions, Wick theorems; Feynman diagrams, self-energy and Dyson equation, polarisation operator and vertex functions.
Perturbation theory for non-zero temperatures, Matsubara frequencies; cluster expansion for the thermodynamic potential; analytic properties of Green functions and frequency summations, linked-cluster theorem.
Time-dependent Green functions at non-zero temperatures, Keldysh-Schwinger formalism.
Graphical representation of the perturbation expansion, Feynman diagrams and their classification, renormalization of the perturbation expansion.
Annotation
Quantum statistical mechanics, second quantization and Fock space, ideal and non-ideal quantum gases, two- particle interaction. Perturbation theory for interacting systems, Matsubara's formalism, analytic properties of perturbation series and of Green's function. Feynman diagrams, Dyson and Bethe-Salpeter equations, Ward identities and simple approximations. Interacting electrons in metals, microscopic basis of the Fermi liquid theory.
For the 1st and 2nd year of the TF and FPL studies and for doctoral students.