We present various approaches to the Anderson lattice model, starting from the limit of infinite spatial dimensions d. In this limit the lattice model can be mapped onto the single impurity model (SI) with an effective density of states determined from a selfconsistence condition (SCC). Similar approaches to the lattice in 3d were based on the non crossing approximation (NCA) for the SI, but differed in the SCC used. Relations between the different SCCs and new ones are given, results for transport quantities are discussed. A diagrammatical derivation of the SCC in infinite d is improved by including d−1corrections.

Transport properties of the Anderson lattice model are obtained from an extension of the single impurity equations to the lattice, taking advantage of the limit of infinite spatial dimensions. A single resolvent formalism is used, and only the simplest lattice processes are included in the calculation.

A new scheme of self-consistent integral equations for the Anderson lattice model is set up and exploited for a calculation of the density of states and of transport coefficients like resistivity and thermoelectric power. It generalizes the noncrossing approximation (NCA) for the single-impurity model by incorporating lattice effects in a local approximation, valid for large spatial dimensions, and concentrates on the simplest contribution for the self-energy correction due to the lattice. A formation of a hybridization gap at the Fermi level is seen as well as a tendency to fulfill Luttinger's theorem. A pronounced maximum of the resistivity and a sign-change of the thermoelectric power are obtained.

The influence of the lattice on the density of states for conduction-band andf-electrons in heavy fermion and mixed valent systems has been calculated from an extension of the non-crossing approximation to the lattice. It is shown that the main features of such a calculation can be obtained by a simple numerical simulation.