$\frac{t}{U}$ expansion for the Hubbard model

We describe a unitary transformation which eliminates terms coupling states with differing numbers of doubly occupied sites from the Hamiltonian of the Hubbard model. The $S$ matrix for the transformation, and the transformed Hamiltonian, $H^{\prime }$, are generated by an iterative procedure which results in an expansion in powers of the hopping integral $t$ divided by the on-site energy $U$. For a half-filled band and in the space with no doubly occupied sites, $H^{\prime }$ is equivalent to a spin Hamiltonian. We discuss the implications of our results for $H^{\prime }$ on theories of high-temperature superconductivity.