Perturbation Theory for an Infinite Medium of Fermions. III. Derivation of the Landau Theory of Fermi Liquids

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Abstract
The methods employed in the previous papers of this series for the ground-state energy of a normal Fermion system are extended to finite temperatures. The basic assumption is that the density matrix of the actual system in thermodynamic equilibrium can be derived by adiabatic transformation from the density matrix of system of noninteracting particles at the same temperature, volume, and chemical potential. However, the spectrum of the noninteracting system must be dependent on the intensive parameters. The self-consistency of the scheme is exhibited by demonstrating that the effective potential characterizing this system can be related to the self-energy operator of the actual system. Two equivalent versions of the theory are derived. In one of these the basic equations are precisely those of the Landau theory of Fermi liquids with the difference, however, that all quantities are given explicitly from first principles.