(42 Lectures + 14 Tutorial) 

1. Review of second quantisation, one and two body operators, mean field solutions of interacting systems.
2. CanonicalTransformation: Jordan-Wigner, Bogoliubov-Valetin, SchriefferWolf,etc.
3. Green's function formalism at zero & finite temperatures, observables and their relationship to one and two body Greens functions.
4. Thermodynamic potential, spectral functions, analytic properties of Green’s function.
5. Linear Response, correlation function, sum rules.
6. Green’s functions equation of motion.
7. Diagrammaticperturbationtheory for Greenfunction and the thermodynamic potential. Interacting fermions: Hartree-Fock, Random phase and ladder approximation, Goldstone theorem, Luttinger Ward identities. Interacting bosons: condensate depletion.
8. Functional methods: Imaginary time and coherent state path integrals, many particle partition function and perturbation theory in path integral approach. Stationary phase approximation. Hubbard-Stratonovich transformationand auxiliary field representation of time evolution operator and the partition function. Saddle point approximation and small fluctuation corrections.