  Loop corrections to unequal-time correlation functions in Minkowski spacetime
exhibit secular growth due to a breakdown of time-dependent perturbation
theory. This is analogous to secular growth in equal-time correlators on
time-dependent backgrounds, except that in Minkowski the divergences must not
signal a real IR issue. In this paper, we calculate the late-time limit of the
two-point correlator for different massless self-interacting scalar quantum
field theories on a Minkowski background. We first use a late-time version of
the in-in path integral starting in the vacuum of the free theory; in this
limit, the calculation, including UV renormalization, reduces to that in
in-out. We find linear or logarithmic growth in time, depending on whether the
interaction strength is dimension-one or dimensionless, respectively. We next
develop the Weisskopf-Wigner resummation method, that proceeds by demanding
unitarity within a truncated Hilbert space, to calculate the resummed
correlator and find that it gives an exact exponentiation of the late-time
perturbative result. The resummed (unequal-time) correlator thus decays with an
exponential or polynomial time-dependence, which is suggestive of `universal'
behavior that depends on the dimensions of the interaction strength.
