Abstract: The propagator of the Wigner function is constructed from the WignerLiouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) [1], we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation.