Abstract
It is suggested that bound states can emerge in field theory as alternate solutions to the Bethe-Salpeter equation, not corresponding to the Neumann-series (perturbation-theory) solution. These new solutions are asymptotically similar to elementary-particle solutions and imply nonperturbative anomalous dimensions in the Wilson operator-product expansion. For Goldstone bosons in standard quark models as well as for certain solvable ladder models, these are the only bound-state solutions.