Applying the linear δ-expansion to disordered systems

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.