Quantum Darboux theorem

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