论文标题
在三维形式的统一空间中，具有线性依赖的对称算子的二阶可促进系统分类
Toward Classification of 2nd Order Superintegrable Systems in 3-Dimensional Conformally Flat Spaces with Functionally Linearly Dependent Symmetry Operators
论文作者
论文摘要
我们在三维综合扁平空间上对二阶可促进系统进行分类的重大进展，这些空间具有线性依赖（FLD）对称发生器，并特别强调了复杂的欧几里得空间。这些系统的对称性仅在允许系数取决于空间坐标时才线性依赖。 CALOGERO-MOSER系统在一条线上有3个物体和2参数合理的潜力是FLD可整合系统的最著名示例。我们在3D共同平坦的空间上阐明了这些FLD系统的结构理论，例如，它们始终承认一阶对称性。给出了FLD系统在复杂3D欧几里得空间上的部分分类。这是一个项目的一部分，旨在将所有3D 2阶可整合系统分类在统一空间上。
We make significant progress toward the classification of 2nd order superintegrable systems on 3-dimensional conformally flat space that have functionally linearly dependent (FLD) symmetry generators, with special emphasis on complex Euclidean space. The symmetries for these systems are linearly dependent only when the coefficients are allowed to depend on the spatial coordinates. The Calogero-Moser system with 3 bodies on a line and 2-parameter rational potential is the best known example of an FLD superintegrable system. We work out the structure theory for these FLD systems on 3D conformally flat space and show, for example, that they always admit a 1st order symmetry. A partial classification of FLD systems on complex 3D Euclidean space is given. This is part of a project to classify all 3D 2nd order superintegrable systems on conformally flat spaces.
