Projection operator method in the theory of disordered systems. I. Spectra of quasiparticles

A new method for calculating spectra of disordered systems is developed. It is based on the projection operator technique in which multiple-occupancy corrections are taken automatically into account. The explicit expansion in powers of the interaction is obtained for the self-energy of configurationally averaged Green's function. It is shown that this expansion (distinct from the cumulant series) can be easily summed up in the cluster approximation. For electrons interacting by means of arbitrary potential with chaotically distributed scattering centres closed systems of equations for the electron spectrum are obtained taking into account the scattering on isolated centres and pairs of impurities.