Forward-backward semiclassical dynamics without prefactors

Using a forward-backward representation of all degrees of freedom in a system, we present a rigorous formulation of semiclassical correlation functions or expectation values where the contribution of the prefactor is compensated for by the semiclassical phase. This procedure eliminates the need for computing the semiclassical prefactor whose determination amounts to evaluating the full stability matrix, resulting in a scheme that scales linearly with the number of degrees of freedom. Numerical calculations show that, while some interference is lost, the scheme is capable of capturing most features important to the vibrational dynamics and spectroscopy of multidimensional systems.