  We study quantum field models in indefinite metric. We introduce the modified
Wightman axioms of Morchio and Strocchi as a general framework of indefinite
metric quantum field theory (QFT) and present concrete interacting relativistic
models obtained by analytical continuation from some stochastic processes with
Euclidean invariance. As a first step towards scattering theory in indefinite
metric QFT, we give a proof of the spectral condition on the translation group
for the relativistic models.
