二阶超对称的射影几何
Projective geometry of second-order supersymmetry
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中文总结 AI 辅助
本文提出二阶超对称的射影几何表述，利用射影联络和矢量场确定伙伴哈密顿量，并给出光滑延拓判据，通过拉梅对展示与Gelfand-Dikii-Virasoro结构的联系。
中文摘要 AI 辅助
我们证明量子力学中无反常的二阶超对称（SUSY）允许一种射影几何表述，该表述由射影联络和保持它的矢量场给出。一旦物理坐标和能量原点被固定，这些数据决定伙伴哈密顿量和超荷；该场的二次不变量确定中心参数和候选单态能量。该场的不动点结构为量子算符通过超势零点的光滑延拓提供了明确判据。经典上虚构的相似变换选取仿射数据，其协变因子生成施瓦茨量子修正。黎曼模型的维度约化通过体积测度重现这些仿射数据，而适应于所选取场的坐标实现了耦合常数变形。一个单隙拉梅对说明了SUSY辅助几何与支配物理解乘积的Gelfand-Dikii-Virasoro结构之间的关系。其Lax-Novikov积分通过射影稳定化子的一阶作用作用于薛定谔解；在无反射极限下，它在物理坐标中与辅助三阶Bol算子成比例。
英文摘要
We show that anomaly-free second-order supersymmetry (SUSY) in quantum mechanics admits a projective-geometric formulation in terms of a projective connection and a vector field preserving it. Once the physical coordinate and energy origin are fixed, these data determine the partner Hamiltonians and supercharges; the field's quadratic invariant fixes the central parameter and candidate singlet energies. The fixed-point structure of this field yields explicit criteria for smooth continuation of the quantum operators through superpotential zeros. The classically fictitious similarity transformation selects affine data whose covariant factors generate the Schwarzian quantum correction. Dimensional reduction of a Riemannian model reproduces these affine data through the volume measure, while a coordinate adapted to the selected field implements coupling-constant metamorphosis. A one-gap Lame pair illustrates the relation between the SUSY auxiliary geometry and the Gelfand-Dikii-Virasoro structure governing physical solution products. Its Lax-Novikov integral acts on Schrodinger solutions through the first-order action of a projective stabilizer; in the reflectionless limit it becomes proportional, in the physical coordinate, to the auxiliary third Bol operator.
发表机构
- Universidad de Santiago de Chile（圣地亚哥智利大学）
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