  In this article we review the construction of local, relativistic quantum
vector fields by analytic continuation of Euclidean vector fields obtained as
solutions of covariant SPDEs. We revise the formulation of such SPDEs by
introducing new Gaussian noise terms -- a procedure which avoids the
re-definition of the two point functions needed in previous approaches in order
to obtain relativistic fields with nontrivial scattering. We describe the
construction of asymptotic states and the scattering of the analytically
continued solutions of these new SPDEs and we give precise conditions for
nontrivial and well-defined scattering.
