QUASI-PARTICLE PSEUDO-HAMILTONIAN OF AN INFINITESIMALLY POLARIZED FERMI-LIQUID

We present the microscopic derivation of a quasiparticle pseudo-Hamilt onian for an infinitesimally polarized electron liquid. The Hamiltonia n is expressed in terms of suitably defined quasiparticle operators. O ur approach is based on a canonical transformation which allows one to replace the bare Coulombic coupling between the interacting electrons with an effective interaction between quasiparticles in which collect ive charge and spin fluctuations are explicitly accounted for. The rel evant matrix elements of the charge and spin-density operators enter o ur theory via linear-response functions: the charge response, the long itudinal and transverse spin responses, and the mixed charge-spin resp onse. These susceptibilities are in turn expressed in terms of the app ropriate many-body local fields. As a consequence our method can be se en as an attempt to satisfactorily include in a self-consistent manner the effects of the vertex corrections associated with charge and spin -fluctuations of the electron liquid. As a result useful expressions f or the quasiparticle energy and the effective interaction between two quasiparticles are determined. These can, in turn, be employed in a mi croscopic determination of the parameters of the Landau theory of the Fermi liquid. The generalization of our results to a multicomponent sy stem is also discussed.