Derivation of the Landau Theory of Fermi Liquids. I. Formal Preliminaries

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Abstract
The formal relationships necessary to derive the Landau theory of Fermi liquids are given. These include relationships between scattering functions for small energy and momentum transfers, vertex functions, and correlation functions. In addition certain identities (of the Ward type in quantum electrodynamics) are established which enable us to evaluate these quantities. Finally, the form of all these relationships when a long-ranged Coulomb force is present is given.