  The limits of direct unitary transformation of many-fermion Hamiltonians are
explored. Practical application of such transformations requires that effective
many-body interactions be discarded over the course of a calculation. The
truncation of the Hamiltonian leads to finite errors and in some cases
divergences. A new formalism is proposed to manage errors and avoid
divergences. Removing all interactions from a many-fermion Hamiltonian reduces
it to fermion number operators allowing for direct calculation of eigenvalues.
If the same transformations are applied to the bare fermions, eigenfermions are
produced whose Slater determinants form eigenstates. This enables a hierarchy
of diagonalization methods of increasing accuracy as fewer interactions are
discarded from the Hamiltonian.
