  We apply the linear $\delta$-expansion (LDE), originally developed as a
nonperturbative, analytical approximation scheme in quantum field theory, to
problems involving noninteracting electrons in disordered solids. The initial
idea that the LDE method might be applicable to disorder is suggested by the
resemblance of the supersymmetric field theory formalism for quantities such as
the disorder-averaged density of states and conductance to the path integral
expressions for the n-point functions of $\lambda\phi^4$ field theory, where
the LDE has proved a successful method of approximation. The field theories
relevant for disorder have several unusual features which have not been
considered before, however, such as anticommuting fields with Faddeev-Popov
(FP) rather than Dirac-type kinetic energy terms, imaginary couplings and
Minkowskian field coordinate metric.Nevertheless we show that the LDE method
can be successfully generalized to such field systems.
