论文标题
量子整合性：拉格朗日1形案例
Quantum integrability: Lagrangian 1-form case
论文作者
论文摘要
一个新的可集成性概念称为具有拉格朗日1形结构的可集成系统的多维一致性，以量子水平的几何语言捕获。零阳光条件意味着多维一致性将是一个关键关系，例如汉密尔顿运营商。因此，零曲面条件的存在直接导致映射的路径无关特征，例如Schrödinger图片中的多次演变。另一个重要的结果是配方连续的多时间传播器。借助这种新型的传播器，不可避免地会出现对所有可能的路径的新观点，因为不仅必须考虑到因变量的空间中的所有可能路径，而且还必须考虑自变量的空间。半古典近似适用于以经典作用和周围的波动来表达的多时间传播器。因此，极端传播器在自变量空间上产生了独立的路径特征，可以保证系统的集成性。
A new notion of integrability called the multi-dimensional consistency for the integrable systems with the Lagrangian 1-form structure is captured in the geometrical language for quantum level. A zero-curvature condition, which implies the multi-dimensional consistency, will be a key relation, e.g. Hamiltonian operators. Therefore, the existence of the zero-curvature condition directly leads to the path-independent feature of the mapping, e.g. multi-time evolution in the Schrödinger picture. Another important result is the formulation of the continuous multi-time propagator. With this new type of the propagator, a new perspective on summing all possible paths unavoidably arises as not only all possible paths in the space of dependent variables but also in the space of independent variables must be taken into account. The semi-classical approximation is applied to the multi-time propagator expressing in terms of the classical action and the fluctuation around it. Therefore, the extremum propagator, resulting in path independent feature on the space of independent variables, would guarantee the integrability of the system.
