Many -body effects in electron liquids with Rashba spin -orbit coupling

The main topic of the present thesis is represented by the many-body effects which characterize the physical behavior of an electron liquid in various realizations. We begin by studying the problem of the response of an otherwise homogeneous electron liquid to the potential of an impurity embedded in its bulk. The most dramatic consequence of this perturbation is the existence of so called Friedel density oscillations. We present calculations of their amplitude valid in two as well as in three dimensions. The second problem we will discuss is that of the correlation effects in a three dimensional electron liquid in the metallic density regime. A number of quasiparticle properties are evaluated: the electron self-energy, the quasiparticle effective mass and the renormalization constant. We also present an analysis of the effective Landé g-factor as well as the compressibility. The effects of the Coulomb interactions beyond the random phase approximation have been treated by means of an approach based on the many-body local field factors theory and by utilizing the latest numerical results of Quantum Monte Carlo numerical simulations. The final chapter includes the results of our extensive work on various aspects regarding the two dimensional Fermi liquid in the presence of linear Rashba spin-orbit coupling. By using a number of many-body techniques, we have studied the interplay between spin-orbit coupling and electron-electron interaction. After proving an extension to the famous Overhauser Hartree-Fock instability theorem, a considerable amount of work will be presented on the problem of the density and spin response functions. For the study of the spin response, we will present the results of extensive numerical calculations based on the time dependent mean field theory approach