  The problem of computing quantum mechanical propagators can be recast as a
computation of a Wilson line operator for parallel transport by a flat
connection acting on a vector bundle of wavefunctions. In this picture the base
manifold is an odd dimensional symplectic geometry, or quite generically a
contact manifold that can be viewed as a "phase-spacetime", while the fibers
are Hilbert spaces. This approach enjoys a "quantum Darboux theorem" that
parallels the Darboux theorem on contact manifolds which turns local classical
dynamics into straight lines. We detail how the quantum Darboux theorem works
for anharmonic quantum potentials. In particular, we develop a novel
diagrammatic approach for computing the asymptotics of a gauge transformation
that locally makes complicated quantum dynamics trivial.
