Connected diagram expansion for lattice hamiltonian models

We present a connected diagram expansion technique for energy eigenvalues in Hamiltonian quantum theory. The technique should be particularly useful for lattice models of the type introduced by Wilson, Kogut and Susskind. The method is illustrated by the example of the quantum Ising model in 1 + 1 dimensions. A path integral formalism is outlined from which these results may be derived: it is based on the formal scattering theory of Gell-Mann and Goldberger.