  A condition on a set of truncated Wightman functions is formulated and shown
to permit the construction of the Hilbert space structure included in the
Morchio--Strocchi modified Wightman axioms. The truncated Wightman functions
which are obtained by analytic continuation of the (truncated) Schwinger
functions of Euclidean scalar random fields and covariant vector (quaternionic)
random fields constructed via convoluted generalized white noise, are then
shown to satisfy this condition. As a consequence such random fields provide
relativistic models for indefinite metric quantum field theory, in dimension 4
(vector case), respectively in all dimensions (scalar case).
