  A comprehensive field theory is developed for superconductors with quenched
disorder. We first show that the matrix field theory, used previously to
describe a disordered Fermi liquid and a disordered itinerant ferromagnet, also
has a saddle-point solution that describes a disordered superconductor. A
general gap equation is obtained. We then expand about the saddle point to
Gaussian order to explicitly obtain the physical correlation functions. The
ultrasonic attenuation, number density susceptibility, spin density
susceptibility and the electrical conductivity are used as examples. Results in
the clean limit and in the disordered case are discussed respectively. This
formalism is expected to be a powerful tool to study the quantum phase
transitions between the normal metal state and the superconductor state.
