Symplectic Radon Transform and the Metaplectic Representation
Maurice A. de Gosson
TL;DR
This paper explores the symplectic Radon transform using the metaplectic representation, providing rigorous proofs and interpreting the inverse as a demarginalization of the Wigner distribution in quantum systems.
Contribution
It offers a comprehensive theoretical framework connecting the symplectic Radon transform with the metaplectic representation, including complete proofs and interpretation in quantum mechanics.
Findings
Rigorous proofs of the symplectic Radon transform in multi-dimensional quantum systems
Interpretation of the inverse Radon transform as demarginalization of the Wigner distribution
Completion of previous theoretical work with full proofs
Abstract
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 inverse Radon transform as a "demarginalization process" for the Wigner distribution. This work completes, by giving complete proofs, a previous Note.
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