# Fermion-field approach to the binary-alloy problem

## Abstract

The single-band model for a random binary alloy with "diagonal disorder" is treated as a quantized fermion field in which the fermions represent substitutions of B atoms for A atoms. The average Green's function of an electron in the alloy is then equivalent to the Green's functions of an electron interacting with a fermion field. Various well-known methods for treating the latter problem are applied to the alloy problem. In particular, we are led to a new diagrammatic formulation of the alloy problem which makes transparent the existence of a simply defined series for the self-energy of the average Green's function and suggests several partial summations which are carried out. Also, the functional-derivative method of fermion-field theory is applied to the alloy problem to derive the Schwartz-Siggia equation for the self-energy. The relation to previous work of Yonezawa and Matsubara, Leath and Goodman, and Schwartz and Siggia is briefly discussed. © 1973 The American Physical Society.