  Construction of skeletonized path integrals for a particle moving on a curved
spatial manifold is considered. As shown by DeWitt, Kuchar and others, while
the skeletonized configuration space action can be written unambiguously as a
sum of Hamilton principal functions, different choices of the measure will lead
to different Schrodinger equations. On the other hand, the Liouville measure
provides a unique measure for a skeletonized phase space path integral, but
there is a corresponding ambiguity in the skeletonization of a path through
phase space. A family of skeletonization rules described by Kuchar and referred
to here as geodesic interpolation is discussed, and shown to behave poorly
under the involution process, wherein intermediate points are removed by
extremization of the skeletonized action. A new skeletonization rule, tangent
interpolation, is defined and shown to possess the desired involution
properties.

General Relativity and Quantum Cosmology;Quantum Physics