Operator identity and applications to models of interacting electrons

By correct reduction of some quartic forms in fermion field operators, I eliminate all but a constant and some quadratic terms. I can use this to transform the Wolff model, of a magnetic impurity in a nonmagnetic metal, into a solvable quadratic form in fermions. Applying the same method (with less justification) to Hubbard's model in three dimensions, I obtain an oversimplified but nevertheless suggestive, and diagonal, Hamiltonian.