  We solve the Bethe-Salpeter equation for two-particle scattering in a
field-theoretical model using two lagrangians related by a field
transformation. The kernel of the equation consists of the sum of all
tree-level diagrams for each lagrangian. The solutions differ even if all four
external particles are put on the mass shell, which implies that observables
calculated by solving the Bethe-Salpeter equation depend on the representation
of the theory. We point out that this violation of the equivalence theorem has
a simple explanation and should be expected for any Bethe-Salpeter equation
with a tree-level kernel. Implications for dynamical models of hadronic
interactions are discussed.
