Symplectic Radon Transform and the Metaplectic Representation

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 s...

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Detalles Bibliográficos
Autor principal: de Gosson, Maurice A.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9222323/
https://www.ncbi.nlm.nih.gov/pubmed/35741482
http://dx.doi.org/10.3390/e24060761
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author de Gosson, Maurice A.
author_facet de Gosson, Maurice A.
author_sort de Gosson, Maurice A.
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description 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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spelling pubmed-92223232022-06-24 Symplectic Radon Transform and the Metaplectic Representation de Gosson, Maurice A. Entropy (Basel) Article 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. MDPI 2022-05-28 /pmc/articles/PMC9222323/ /pubmed/35741482 http://dx.doi.org/10.3390/e24060761 Text en © 2022 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
de Gosson, Maurice A.
Symplectic Radon Transform and the Metaplectic Representation
title Symplectic Radon Transform and the Metaplectic Representation
title_full Symplectic Radon Transform and the Metaplectic Representation
title_fullStr Symplectic Radon Transform and the Metaplectic Representation
title_full_unstemmed Symplectic Radon Transform and the Metaplectic Representation
title_short Symplectic Radon Transform and the Metaplectic Representation
title_sort symplectic radon transform and the metaplectic representation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9222323/
https://www.ncbi.nlm.nih.gov/pubmed/35741482
http://dx.doi.org/10.3390/e24060761
work_keys_str_mv AT degossonmauricea symplecticradontransformandthemetaplecticrepresentation

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