  We discuss Euclidean covariant vector random fields as the solution of
stochastic partial differential equations of the form $DA=\eta$, where $D$ is a
covariant (w.r.t. a representation \tau of $SO(d)$) differential operator with
"positive mass spectrum" and $\eta$ is a non-Gaussian white noise. We obtain
explicit formulae for the Fourier transformed truncated Wightman functions,
using the analytic continuation of Schwinger functions discussed by Becker,
Gielerak and Lugewicz. Based on these formulae we give necessary and sufficient
conditions on the mass spectrum of $D$ which imply nontrivial scattering
behaviour of relativistic quantum vector fields associated to the given
sequence of Wightman functions. We compute the scattering amplitudes explicitly
and we find that the masses of particles in the obtained theory are determined
by the mass spectrum of $D$.
