BOUND-STATE ENERGIES IN THE 1 N EXPANSION

We derive and solve - in an arbitrary number of dimensions - Omnes-typ e equations for bound-state energies in weakly coupled quantum field t heories. We show that, for theories defined in the 1/N expansion, thes e equations are exact to leading order in 1/N. We derive and discuss t he weak coupling and nonrelativistic limits of the Omnes equations. We then calculate the binding energies and effective bound-state couplin gs in (1 + 1), (1 + 2) and (1 + 3)-dimensional O(N)-invariant phi4 the ory. We consider both the scalar and symmetric tensor bound states.