Stability of Stokes data in the continuum limit of time-sliced path integrals

Determine whether the Stokes constants and Lefschetz-thimble intersection numbers of time-sliced polynomial quantum-mechanical path integrals remain stable under refinement of the discretization and converge to well-defined continuum quantities associated with the classical solutions.

Background

The paper proposes extending the finite-dimensional Gauss–Manin and resurgence framework to real-time Feynman path integrals by viewing a time-sliced path integral with a polynomial potential as a multidimensional oscillatory integral. Although the critical values of the discretized action are expected to converge to the actions of continuum classical solutions, the number of critical points grows exponentially with the number of time slices, creating a substantial computational challenge.

A separate unresolved issue concerns the continuum limit itself: the global resurgent data that determine which saddles contribute—the Stokes constants and intersection numbers—may change under discretization refinement. Establishing their stability would be necessary before the proposed algebraic method could reliably identify relevant complex classical paths, adjacency relations, and the corresponding Lorentzian path-integral decomposition in the continuum.