Rigorous forward-backward semiclassical formulation of many-body dynamics

A rigorous, yet practical semiclassical formulation of time correlation functions or expectation values is presented. The main idea is to combine the forward and backward propagation steps into a single semiclassical propagator for those degrees of freedom that are not probed in a calculation, while retaining an explicit two-propagator description of the observable low-dimensional system. The combined forward-backward treatment of the environment naturally leads to extensive cancellation and results in an action that is small on the scale of Planck's constant. As a consequence, the integrand is smooth and thus amenable to Monte Carlo sampling. At the same time, important nonclassical effects terms, arising from interference among multiple bounce solutions of the system component, are fully accounted for.