The equation of motion for the reduced Wigner function of a system coupled to
an external quantum system is presented for the specific case when the external
quantum system can be modeled as a set of harmonic oscillators. The result is
derived from the Wigner function formulation of the Feynman-Vernon influence
functional theory. It is shown how the true self-energy for the equation of
motion is connected with the influence functional for the path integral.
Explicit expressions are derived in terms of the bare Wigner propagator.
Finally, we show under which approximations the resulting equation of motion
reduces to the Wigner-Boltzmann equation