Path integral over branching paths

A heuristic definition is given of a Feynman path integral over branching paths. It is used to solve the Cauchy problem for the model Hartree equation in a closed form. A number of properties of the solution are derived from an integral representation. In particular, the quasiclassical asymptotic behavior, the exact solution in the Gaussian case, and the perturbation series are described. An existence theorem is proved for the simplest path integral over branching paths.