  The non perturbative construction of quantum field models with nontrivial
scattering in arbitrary dimension $d$ of the underlying Minkowski space-time is
much more simple in the framework of quantum field theory with indefinite
metric than in the positive metric case. In particular, there exist a number of
solutions in the physical dimension $d=4$, where up to now no positive metric
solutions are known. Here we review, why this is so, and we discuss some
examples obtained by analytic continuation from the solutions of Euclidean
covariant stochastic partial differential equations (SPDEs) driven by
non-Gaussian white noise.
