I wonder if there is a connection between that path integral formulation of QM, the nature of particles as extended objects, and spacetime. Dynamical Triangulation trys to construct the classical 4D world as a quantum superposition of various kinds of spacetime. Could it be that the path integral formulation of QM is correct only because classical spacetime is a quantum mechanical superposition of various kinds of spacetime? You have every kind of path because you have every kind of spacetime? It seems to me that the connection between paths and spacetime itself is the particles. Somehow particle mediate between the QM of paths and the QM of spacetime. This might indicate that particle are features of spacetime such as boundary holes or genus holes. Then particles themselves might be a quantum mechanical supperposition of various kinds of boundaries or various kinds of genus holes. Any thoughts on this?