The Quantum Darboux Theorem,

• URL: http://arxiv.org/abs/2012.15260v2
• Date: Tue, 12 Jan 2021 18:02:10 GMT
• Title: The Quantum Darboux Theorem,
• Authors: Olindo Corradini, Emanuele Latini and Andrew Waldron
• Abstract summary: The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport. 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" We detail how the quantum Darboux theorem works for anharmonic quantum potentials.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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