2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/202659We consider the tree amplitudes of production of $n_2$ scalar particles by $n_1$ particles of another kind, where both initial and final particles are at rest and on mass shell, in a model of two scalar fields with $O(2)$ symmetric interaction and unequal masses. We find that these amplitudes are zero except for the lowest possible $n_1$ and $n_2$, and that the cancellation of the corresponding Feynman graphs occurs due to a special symmetry of the classical mechanical counterpart of this theory. This feature is rather general and is inherent in various other scalar field theories.11 pages Preprint INR-830/93, August 1993High Energy Physics - Phenomenologytext