Microscopic theory of a normal Fermi liquid at zero temperature

Abstract

The microscopic theory of a Fermi liquid formulated by Mohling and based upon the work of Lee and Yang is used to develop a quasi-particle theory of a Fermi liquid at zero temperature. The energy per particle, the particle momentum distribution, and the transformation function Δ( k) introduced by the Λ-transformation are expanded through third order in the “two-quasi-particle reaction matrix” g 1( k 1 k 2 / k 3 k 4). It is shown that the explicit expressions for the three quantities above satisfy the equations basic to Landau's phenomenological theory of a Fermi liquid term by term, provided Δ( k) is identified as the quasi-particle interaction energy. From this fact, it is concluded that the Λ-transformation introduced by Mohling is actually a transformation from a particle representation to a quasi-particle representation of the system. This approach differs from previous efforts in the fact that the series being generated here is not a perturbation series. In fact, the explicit series obtained in this work bears a striking resemblance to that employed by Brueckner. This similarity is investigated in some detail. An extension of the Landau theory to encompass generalized interaction functions is made. This generalization, in conjunction with the explicit expression for the energy per particle, is then used to examine the “many-quasi-particle” potentials which appear in the Λ-transformed equations.