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
Descripción
Sumario: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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