Many-body effects in electron scattering

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Abstract
When setting up the theory of the transport properties of metals in terms of Landau's theory of quasi-particles, it is necessary to define precisely what is the scattering amplitude of an impurity or phonon for a quasi-particle including all many-body corrections. This is done, and the definition shown to be consistent with the fundamental diagrammatic calculation of the resistivity and with the scattering potential determining the shape of the Fermi surface. The limit of long wavelengths is evaluated in particular, and the results shown to be derivable also by a simple-minded application of the Landau theory. Both the coulomb repulsion and the interaction via virtual phonons are considered. In fact, all phonon effects cancel out from the resistivity and the band structure, a result depending on the special nature of the interaction which we discuss also from the point of view of the Landau theory.