New approaches to the Anderson lattice system

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 different 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{sup -1} corrections.