Interacting disordered electrons and the metal-insulator transition: The field theoretic approach reanalyzed

Abstract

We consider the nonlinear σ-model for the interplay between interaction and disorder in electronic systems as derived by Finkelshtein. We use a parametrization of the model which facilitates setting up a loop expansion in exact analogy to more common models. We discuss symmetry properties, and address the questions of renormalizability and the number of renormalization constants. For the model with unitary symmetry we calculate the one-point and various two-point vertex functions to one-loop order. The introduction of five renormalization constants is necessary to make these finite. The three-point vertex functions are then shown to be rendered finite by the same five renormalization constants. This is a very strong indication that the theory is renormalizable, and that the resulting RG flow equations are physically meaningful.