  A general field-theoretical description of many-fermion systems, with or
without quenched disorder, is developed. Starting from the Grassmannian action
for interacting fermions, we first bosonize the theory by introducing composite
matrix variables that correspond to two-fermion excitations and integrating out
the fermion degrees of freedom. The saddle point solution of the resulting
matrix field theory reproduces a disordered Hartree-Fock approximation and an
expansion to Gaussian order about the saddle point corresponds to a disordered
RPA-like theory. In the clean limit they reduce to the ordinary Hartree-Fock
and random-phase approximations. We first concentrate on disordered systems,
and perform a symmetry analysis that allows for a systematic separation of the
massless modes from the massive ones. By treating the massive modes in a simple
approximation, one obtains a technically satisfactory derivation of the
generalized nonlinear sigma-model that has been used in the theory of
metal-insulator transitions. The theory also allows for the treatment of other
phase transitions in the disordered Fermi liquid. We further use
renormalization group techniques to establish the existence of a disordered
Fermi-liquid fixed point, and show that it is stable for all dimensions d>2.
The so-called weak-localization effects can be understood as corrections to
scaling near this fixed point. The general theory also allows for studying the
clean limit. For that case we develop a loop expansion that corresponds to an
expansion in powers of the screened Coulomb interaction, and that represents a
systematic improvement over RPA. We corroborate the existence of a Fermi-liquid
fixed point that is stable for all dimensions d>1, in agreement with other
recent field-theoretical treatments of clean Fermi liquids.
