We calculate the overlap between two many-body wave functions for a superfluid film containing a vortex at shifted positions. Comparing the results to phenomenological theories, which treat vortices as point particles, we find that the results are consistent if the point-particle vortices are considered as under the action of the Magnus force and in weak interaction with sound waves of the superfluid. We are then able to resolve the disagreement concerning the effective mass of vortices, showing it is finite.