  We demonstrate the power of a first principle-based and practicable method
that allows for the perturbative computation of reduced density matrix elements
of an open quantum system without making use of any master equations. The
approach is based on techniques from non-equilibrium quantum field theory like
thermo field dynamics, the Schwinger-Keldsyh formalism, and the Feynman-Vernon
influence functional. It does not require the Markov approximation and is
essentially a Lehmann-Szymanzik-Zimmermann-like reduction. In order to
illustrate this method, we consider a real scalar field as an open quantum
system interacting with an environment comprising another real scalar field. We
give a general formula that allows for the perturbative computation of density
matrix elements for any number of particles in a momentum basis. Finally, we
consider a simple toy model and use this formula to obtain expressions for some
of the system's reduced density matrix elements.
