Axioms for the category of Hilbert spaces

We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the mathematical foundations of quantum theory raised in reconstr...

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Detalles Bibliográficos
Autores principales: Heunen, Chris, Kornell, Andre
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2022
Materias:
Physical Sciences
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8892366/
https://www.ncbi.nlm.nih.gov/pubmed/35217613
http://dx.doi.org/10.1073/pnas.2117024119
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author Heunen, Chris
Kornell, Andre
author_facet Heunen, Chris
Kornell, Andre
author_sort Heunen, Chris
collection PubMed
description We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the mathematical foundations of quantum theory raised in reconstruction programs such as those of von Neumann, Mackey, Jauch, Piron, Abramsky, and Coecke.
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spelling pubmed-88923662022-08-25 Axioms for the category of Hilbert spaces Heunen, Chris Kornell, Andre Proc Natl Acad Sci U S A Physical Sciences We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. The axioms are purely categorical and do not presuppose any analytical structure. This addresses a question about the mathematical foundations of quantum theory raised in reconstruction programs such as those of von Neumann, Mackey, Jauch, Piron, Abramsky, and Coecke. National Academy of Sciences 2022-02-25 2022-03-01 /pmc/articles/PMC8892366/ /pubmed/35217613 http://dx.doi.org/10.1073/pnas.2117024119 Text en Copyright © 2022 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Physical Sciences
Heunen, Chris
Kornell, Andre
Axioms for the category of Hilbert spaces
title Axioms for the category of Hilbert spaces
title_full Axioms for the category of Hilbert spaces
title_fullStr Axioms for the category of Hilbert spaces
title_full_unstemmed Axioms for the category of Hilbert spaces
title_short Axioms for the category of Hilbert spaces
title_sort axioms for the category of hilbert spaces
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8892366/
https://www.ncbi.nlm.nih.gov/pubmed/35217613
http://dx.doi.org/10.1073/pnas.2117024119
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