An action principle for complex quantum trajectories

In a recent paper [B. Poirier, Chem. Phys. 370, 4 (2010)], a formulation of quantum mechanics was presented for which the usual wavefunction and Schrdinger equation are replaced with an ensemble of real-valued trajectories satisfying a principle of least action. It was found that the resultant quantum trajectories are those of Bohmian mechanics. In this paper, analogous ideas are applied to Bohmian Mechanics with Complex Action (BOMCA). The standard BOMCA trajectories as previously defined are found not to satisfy an action principle. However, an alternate set of complex equations of motion is derived that does exhibit this desirable property, and an approximate numerical implementation is presented. Exact analytical results are also presented, for Gaussian wavepacket propagation under quadratic potentials.