流形的内禀动力学：量子路径、完整性和轨迹局部化
Intrinsic Dynamics of Manifolds: Quantum Paths, Holonomy, and Trajectory Localization
摘要：
我们认为一个“积分”的经典概念的仿射联络提供了一个对应的路径之间的流形和流形的仿射同态的扩展。这些路径同态是通过连接沿着路径的平行移动的推广。用这种方法，可以平移非解析函数和分布，而不是切向量。我们描述了积分完整性和积分曲率。在辛或量子层次上，这种构造构成了辛或量子路径，以及量子连接，量子曲率和量子完整性。构造路径同态，应用于一个给定的动力系统的轨迹，产生一个系统的转换到一个新的，它有一个先验选择的平衡点。在辛（量子）的情况下，这种动态局域化提供了量子流的相干型表示。
英文摘要：
We consider an ``integral'' extension of the classical notion of affine connection providing a correspondence between paths in the manifold and diffeomorphisms of the manifold. These path-diffeomorphisms are a generalization of parallel translations along paths via the connection. In this way, one can translate nonanalytic functions and distributions rather than tangent vectors. We describe the integral holonomy and the integral curvature. On the symplectic or quantum level this construction makes up the symplectic or quantum paths, as well quantum connection, quantum curvature and quantum holonomy. The construction of path-diffeomorphisms, being applied to trajectories of a given dynamical system produces a transformation of the system to a new one which has an a priori chosen equilibrium point. In the symplectic (quantum) case, this dynamic localization provides a coherent-type representation of the quantum flow.
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