Symplectic Radon Transform and the Metaplectic Representation

被引：5
作者：
de Gosson, Maurice A. [1 ]
机构：
[1] Univ Vienna, Fac Math NuHAG, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
来源：
ENTROPY | 2022年 / 24卷 / 06期
关键词：
radon transform; metaplectic group; Lagrangian planes; symplectic tomography; QUANTUM; STATES;
D O I：
10.3390/e24060761
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study the symplectic Radon transform from the point of view of the metaplectic representation of the symplectic group and its action on the Lagrangian Grassmannian. We give rigorous proofs in the general setting of multi-dimensional quantum systems. We interpret the Radon transform of a quantum state as a generalized marginal distribution for its Wigner transform; the inverse Radon transform thus appears as a "demarginalization process" for the Wigner distribution.
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页数：13
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