Properties of the path-class expansion in the continuous limit

We investigate the properties of the previously introduced path-class expansion, a method for the calculation of the non-Born-Oppenheimer dynamics of molecules and solid states, in the limit of infinitesimal step-size. It is found that in this limit the class-average functions obey Schrِdinger-like equations of motion. This gives rise to a new interpretation of the path-class formalism as an averaging over approximately separable physical systems. For certain model systems and path classes the equations of motion can be solved analytically. This leads to an easily evaluated approximation for the description of the dynamics of the spin-boson system.