Analytic perturbation theory and localization phenomena

This paper attempts to apply the results of analytic perturbation theory to systems exhibiting some degree of randomness in their state variables. In particular, we focus on the localization problem in the Anderson model. It is shown that this approach proves the existence of bound states as a result of the statistical treatment of the Weinberg–van Winter–Hunziker irreducible N-particle kernel. The analysis is extended beyond the one-particle cluster approach and the occurrence of higher-order clusters is discussed in relation to the diluteness criterion and the conditions set on the interaction potential V.