  We consider the one-particle sector of the spinless Yukawa model, which
describes the interaction of a nucleon with a real field of scalar massive
bosons (neutral mesons). The nucleon as well as the mesons have relativistic
dispersion relations. In this model we study the dependence of the nucleon mass
shell on the ultraviolet cut-off $\Lambda$. For any finite ultraviolet cut-off
the nucleon one-particle states are constructed in a bounded region of the
energy-momentum space. We identify the dependence of the ground state energy on
$\Lambda$ and the coupling constant. More importantly, we show that the model
considered here becomes essentially trivial in the limit $\Lambda\to\infty$
regardless of any (nucleon) mass and self-energy renormalization. Our results
hold in the small coupling regime.
