Many Body Theory 1

The main objective of the course is to provide an accurate presentation of important techniques needed in the study of many-particle systems in condensed matter, statistical mechanics, nuclear physics. It is a course in non-relativisti, low-energy field theory, with many particles. The main topics are: second quantization, Hartree-Fock equations, the Gell-Mann and Low theorem, Wick's theorem, time-ordered and retarded Green functions, Feynman's diagrams, Dyson equations and resummation of Hartree and RPA terms, Hedin's equations, linear response theory, quasiparticles. The theory is illustrated by applications to
The homogeneous electron gas.

To write operators in second quantization.
The comprehension of the Hartree Fock approximation, and knowledge of the HF properties of the electron gas.
The meaning of T-ordered and retarded Green funcions, and their relation in frequency space. To evaluate a Lehmann expansion.
To pass from an equation of motion to a Dyson equation. The structure of poles and their meaning.
The meaning of normal ordering and contraction, and the conditions for the validity of Wick's theorem, evaluation of correlators.
Knowledge of the Feynman rules and their origin. To write the analytic expression of a Feynman diagram in x and k spaces.
Meaning of the generalized dielectric function, and of the RPA approximation.
To know and apply the linear response theory.
Evaluate the effective mass and the dispersion law of a quasiparticle.