
Interacting electrons in metals
I.V. Bobkova

Oneparticle Green’s function (Non interacting fermions)
 Verbal definition of retarded oneparticle Green’s function.
 An example for Green’s function diagram expansion.
 Advanced Green’s function

Oneparticle Green’s function (Interacting fermions)
 Formal definition of oneparticle Green’s function.
 Hamiltonian and graphic representation of the interaction between fermions.
 Quasi particles in HartreeFock approximation.
 Back to quasi particles.
 Diagrams topology.

Dyson equation.
 Derivation of the Dyson equation.
 Ladder approximation
 Quasi particles in random phase approximation.
 Polarization operator in common case.

Justification of Fermi liquid.
 Self consistent perturbation theory.
 Quasi particles and oneparticle Green’s function.
 Dressed vertex.

Ground state energy in random phase approximation.
 Vacuum amplitude
 Calculation of the ground state energy.

Two particle propagator.
 Definition of two particle propagator
 Plasmons.
 Vertex function and scattering of quasi particles.
 Excitons.

Green’s functions at finite temperature.
 Formulation of the problem.
 Perturbation theory for the Matsubara Green;s function.
 Matsubara Green’s function foe free particles.

Green's functions in the theory of superconductivity.
 Hamiltonian of interacting electrons and phonons.
 Ground state energy, quasiparticles (based on the BCS method).
 Nonapplicability of the standard perturbation diagram expansion.
 Formalism Nambu.
Main references
 Mattuck R., A guide to Feynman diagrams in the many body problem, McGrawHill Publishing Company Limited, 1967.
 L.S. Levitov and A.V. Shytov, Green's functions. Theory and practice, FizMatLitNauka, Moscow, 2003 (in russian).
Further reading
 A.A. Abrikosov, L.P. Gor'kov, and I.Ye. Dzyaloshinskii, Quantum field theoretical methods in statistical physics, Pergamon Press, 1965
 V.M. Galitskii, ZhETF, 34, 151 (1958).
