Perturbation theory for the periodic Anderson model

We investigate the system of conductivity electrons and f-localized electrons described by the periodic Anderson model. Single-site hybridization of the state of two constituent subsystems of electrons is treated as a perturbation. We develop a new diagram technique based on the use of multiparticle one-site irreducible Green’s functions for the f-electrons and the standard Wick theorem for the subsystem of conductivity electrons. We derive the Dyson equations for the one-particle Green’s functions and find the relation between these functions. These results are exact and can be used as a starting point for self-consistent approximations. In the Hubbard-I approximation, we analyze the spectrum of one-particle perturbations. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 2, pp. 308–322, February, 1997.