Renormalizability of the density of states of interacting disordered electron system

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Abstract
A perturbative analysis of the single-particle density of states for an interacting disordered Fermion system is carried out up to second order both in the inverse conductance and in the interaction when the singularity in the particle-particle channel is suppressed. By imposing the renormalizability condition in two dimensions on our perturbative expression of the single-particle density of states, we obtain the group equation for a particular combination of the effective couplings due to the interaction at first order in the inverse conductance. This result agrees with the one obtained from the one-loop analysis of the effectivefield theoretic Lagrangian obtained by Finkel'stein for the same system. The present calculation is the only available check of that theory at second order in the inverse conductance.