  Considering disordered electron systems we suggest a scheme that allows us to
include an electron-electron interaction into a supermatrix sigma-model. The
method is based on replacing the initial model of interacting electons by a
fully supersymmetric model. Although this replacement is not exact, it is a
good approximation for a weak short range interaction and arbitrary disorder.
The replacement makes the averaging over disorder and further manipulations
straightforward and we come to a supermatrix sigma-model containing an
interaction term. The structure of the model is rather similar to the replica
one, although the interaction term has a different form. We study the model
making perturbation theory and renormalization group calculations. We check the
renormalizability of the model in the first loop approximation and in the first
order in the interaction. In this limit we reproduce the renormalization group
equations known from earlier works. We hope that the new supermatrix
sigma-model may become a new tool for non-perturbative calculations for
disordered systems with interaction.
