Matrix field theory for disordered electron systems. A useful formalism fo perturbative expansions

Matrix field theories (MFT) have recently been used to describe the metal-insulator transition for interacting disordered electrons. With a suitable parametrization of the field we show a correspondence between these models and the usual many-body perturbation theory. By use of this correspondence it is easier to perform two-loop calculations of the physical quantities. For some of these quantities this technique has already been used but not explicitly described. Our task is to put forward in an explanatory way the main aspects of this formalism. As an application we explicitly perform the two-loop expansion of the single-particle density of states (DOS) in the particular case when magnetic impurities are present. Such calculations turn out to be consistent with the prediction of the first order renormalization group (RG) scaling equations. © 1988