论文标题
量子darboux定理，
The Quantum Darboux Theorem,
论文作者
论文摘要
计算量子机械传播器的问题可以作为对威尔逊线运算符的计算，该计算通过作用在波形矢量束上的平面连接来平行运输。在这张图片中，基本歧管是一个奇怪的符号符号几何形状，或者是相当普遍的接触歧管，可以将其视为“相位空间”，而纤维是希尔伯特的空间。这种方法享有一种“量子darboux定理”，与触点歧管上的darboux定理相似，该定理将局部古典动力学变成直线。我们详细介绍了量子darboux定理如何适用于非谐量子电位。特别是，我们开发了一种新颖的示意方法，用于计算局部变化的渐近变换的渐近学方法，该方法在局部使复杂的量子动力学微不足道。
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.
