AI 中文总结
该研究基于辛群传递作用建立拉格朗日Radon变换的辛形式，将Wigner变换边际扩展至任意拉格朗日子空间，统一处理辛旋转关联的位置与动量测量，解决Pauli重构问题并建立密度算子重构公式。
AI 中文摘要
我们基于辛群在拉格朗日格拉斯曼流形上的传递作用，建立了拉格朗日Radon变换的辛形式。该几何框架将Wigner变换的经典边际概念（视为基本层析图）自然扩展到任意拉格朗日子空间。所得广义层析成像统一处理了通过辛旋转关联的位置和动量测量。作为应用，我们重新审视Pauli重构问题，建立了从广义拉格朗日层析图重构密度算子的公式。
英文摘要
We develop a symplectic formulation of the Lagrangian Radon transform based on the transitive action of the symplectic group on the Lagrangian Grassmannian. This geometric framework naturally extends the classical notion of the marginals of the Wigner transform, viewed as elementary tomograms, to arbitrary Lagrangian subspaces. The resulting generalized tomography provides a unified treatment of position and momentum measurements related by symplectic rotations. As applications, we revisit the Pauli reconstruction problem and establish reconstruction formulas for density operators from generalized Lagrangian tomograms.
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