Pair Theory of the Hubbard Hamiltonian

A pair theory of the Hubbard Hamiltonian is presented for the case of a half-filled band. The original Hamiltonian is reformulated exactly in terms of pair operators which satisfy boson commutation relations. The pair energies and wave functions are obtained explicitly. In the one-dimensional case, these reduce to the results derived by Lieb and Wu for $M=1\mathrm{}$. The pair Hamiltonian offers a better starting point for perturbation treatments or variational calculations.