Proper weak-coupling approach to the periodic s-d(f) exchange model

The periodic s-d(f) exchange model is characterized by a wide variety of interesting applications, a simple mathematical structure and a limited number of reliable approximations which take care of the quantum nature of the participating spins. We suggest the use of a projection-operator method for getting information perturbationally, which are not accessible via diagrammatic approaches. In this paper we present in particular results beyond perturbation theory, which are obtained such that almost all exactly known limiting cases are incorporated correctly. We discuss a variety of possible methods and evaluate their consequences for one-particle properties. These considerations serve as a guideline for a more effective approach to the model.