  The recently established generalized Gell-Mann--Low theorem is applied in
lowest perturbative order to bound-state calculations in a simple scalar field
theory with cubic couplings. The approach via the generalized Gell-Mann--Low
Theorem retains, while being fully relativistic, many of the desirable features
of the quantum mechanical approaches to bound states. In particular, no
abnormal or unphysical solutions are found in the model under consideration.
Both the non-relativistic and one-body limits are straightforward and
consistent. The results for the spectrum are compared to those of the
Bethe-Salpeter equation (in the ladder approximation) and related equations.
