Critical behavior of the density of states at the metal-insulator transition

We perform a thorough analysis of the critical behavior of the density of states at the metal-insulator transition within the framework of the field-theoretic renormalization group. Of the previous, conflicting results obtained by resumming the perturbation theory, and by frequency-momentum-shell renormalization-group methods, we agree with the one yielding conventional power-law behavior. Emphasis is placed on a detailed technical derivation of this result, and on peculiarities in the renormalization-group description that arises from the long-ranged nature of the Coulomb interaction, and from the presence of multiple time scales in the problem.