Scattering behaviour of quantum vector fields obtained from Euclidean covariant SPDEs

We discuss Euclidean covariant vector random fields as the solution of stoc hastic partial differential equations of the form DA = eta, where D is a co variant (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 ex plicit formulae for the Fourier transformed truncated Wightman functions, u sing the analytic continuation of Schwinger functions discussed by Becker, Gielerak and Lugewicz. Based on these formulae we give necessary and suffic ient conditions on the mass spectrum of D which imply nontrivial scattering behaviour of relativistic quantum vector fields associated to the given se quence of Wightman functions. We compute the scattering amplitudes explicit ly and we find that the masses of particles in the obtained theory are dete rmined by the mass spectrum of D.