Theory of the Anderson impurity model: The Schrieffer– Wolff transformation re–examined.’ preprint HD–TVP–95–14, ESI–prepint 270, condmat/9510145

We apply the method of innitesimal unitary transformations recently introduced by Wegner [1] to the Anderson single impurity model. It is demonstrated that this method provides a good ap-proximation scheme for all values of the on-site interaction U, it becomes exact for U = 0. We are able to treat an arbitrary density of states, the only restriction being that the hybridization should not be the largest parameter in the system. Our approach constitutes a consistent framework to derive various results usually obtained by either perturbative renormalization in an expansion in the hybridization?, Anderson's \poor man's " scaling approach or the Schrieer{Wol unitary transformation. In contrast to the Schrieer{Wol result we nd the correct high{energy cuto and avoid singularities in the induced couplings. An important characteristic of our method as compared to the \poor man's " scaling approach is that we continuously decouple modes from the impurity that have a large energy dierence from the impurity orbital energies. In the usual scaling approach this criterion is provided by the energy dierence from the Fermi surface.