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A diagrammatic technique for two-particle vertex functions is used todescribe systematically the influence of spatial quantum coherence andbackscattering effects on transport properties of noninteracting electrons in arandom potential. In analogy with many-body theory we construct parquetequations for topologically distinct {\em nonlocal} irreducible vertexfunctions into which the {\em local} one-particle propagator and two-particlevertex of the coherent-potential approximation (CPA) enter as input. Tocomplete the two-particle parquet equations we use an integral form of the Wardidentity and determine the one-particle self-energy from the known irreduciblevertex. In this way a conserving approximation with (Herglotz) analyticaveraged Green functions is obtained. We use the limit of high spatialdimensions to demonstrate how nonlocal corrections to the $d=\infty$ (CPA)solution emerge. The general parquet construction is applied to the calculationof vertex corrections to the electrical conductivity. With the aid of thehigh-dimensional asymptotics of the nonlocal irreducible vertex in theelectron-hole scattering channel we derive a mean-field approximation for theconductivity with vertex corrections. The impact of vertex corrections onto theelectronic transport is assessed quantitatively within the proposed mean-fielddescription on a binary alloy.Comment: REVTeX 19 pages, 9 EPS diagrams, 6 PS figure

Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons