ABSTRACT

This chapter describes the Green's function formalism of electron gas in the presence of an impurity with the main aim being introduction of the diagrammatic perturbation theory. The diagrammatic perturbation theory can be a useful technique in solving the problem of electrons propagating in a disordered system. The chapter examines all diagrams leading to the formal expansion of the Green's function in powers of the impurity potential. It considers a finite density of impurities where the perturbation series as well as the Green's function depend on the exact position of each of the impurities, which implies that the exact microscopic properties are dependent on the exact realization of disorder. The chapter introduces the concept of the average electronic self-energy to enable us to understand the interacting environment feedback on a propagating particle. The average electronic Green's function of a fermion in an interacting environment can be achieved by grouping all scattering processes into the average electronic self-energyΣ¯κ→,ω:.