  A quantum system that interacts with an environment generally undergoes
non-unitary evolution described by a non-Markovian or Markovian master
equation. In this paper, we construct the non-Markovian Redfield master
equation for a quantum scalar field that interacts with a second field through
a bilinear or nonlinear interaction on a Minkowski background. We use the
resulting master equation to set up coupled differential equations that can be
solved to obtain the equal-time two-point function of the system field. We show
how the equations simplify under various approximations including the Markovian
limit, and argue that the Redfield equation-based solution provides a
perturbative resummation to the standard second order Dyson series result. For
the bilinear interaction, we explicitly show that the Redfield solution is
closer to the exact solution compared to the perturbation theory-based one.
Further, the environment correlation function is oscillatory and non-decaying
in this case, making the Markovian master equation a poor approximation. For
the nonlinear interaction, on the other hand, the environment correlation
function is sharply peaked and the Redfield solution matches that obtained
using a Markovian master equation in the late-time limit.
