In trying to find a better approach to the Hubbard and other strongly correlated models, the Wolff model, an impurity model closely related to the Hubbard's model, was reconsidered. A simple solution of this model (and of any other impurity model) in 3 steps was proposed. Firstly, use finite temperature to eliminate the small momentum singularities. Secondly, construct a new representation of the model that associates one auxiliary fermion to each point of the spectrum of the local Green's function. Thirdly, approximate this representation with a finite number of auxiliary fermions to arbitrary precision. The outcome is a terminator dependent Hamiltonian that devises Kondo crossover without Wilson's renormalization group. Because the Hamiltonian only involves a small number of fermions, one has reduced the Kondo problem to the interaction of a small number of fermions.
Applications include the nuclear magnetic resonance (NMR) response of impurity systems, strongly correlated lattice models in the limit of infinite dimension, calculation of interaction between 2 impurities in a metal and an extension of this work to magnetic tunnelling microscopy seems possible.