  We study the properties of strongly interacting massive quantum fields in
space-time as resulting from a parametric decay of the fields with a large
decay width $\gamma$. The resulting imaginary part of the retarded and advanced
propagators in this case is of Lorentzian form and the theory conserves
microcausality, i.e. the commutator between the fields vanishes for space-like
distances in space-time. However, when considering separately space-like and
time-like components of the spectral function in momentum space we find
microcausality to be violated for each component separately. This implies that
the modeling of effective field theories for strongly interacting systems has
to be considered with great care and restrictions to time-like four momenta in
case of broad spectral functions have to be ruled out. Furthermore, when
employing effective propagators with a width $\gamma({\bf p}^2)$ depending
explicitly on three-momentum ${\bf p}$ the commutator of the fields no longer
vanishes for $r>t$ since the related field theory becomes nonlocal and violates
microcausality.
