Generalized Gell-Mann Theorem Applied to a Scalar Model

The recently established generalization of the Gell-Mann-Low theorem is applied to Wick-Cutkosky-like models, where the exchanged particle can have arbitrary mass. We derive the effective Schrödinger equation to lowest non-trivial order, identify the diagrams corresponding to the Bloch-Wilson Hamiltonian, and consider the non-relativistic and one-body limits.