Related papers: Axioms for the category of Hilbert spaces

Axioms for the category of Hilbert spaces

URL: http://arxiv.org/abs/2109.07418v3
Date: Tue, 22 Mar 2022 12:35:45 GMT
Title: Axioms for the category of Hilbert spaces
Authors: Chris Heunen, Andre Kornell
Abstract summary: We provide axioms that guarantee a category is equivalent to that of continuous linear functions between Hilbert spaces. This addresses a question about the mathematical foundations of quantum theory raised in reconstruction programmes such as those of von Neumann, Mackey, Jauch, Piron, Abramsky, and Coecke.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: 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 programmes such as those of von Neumann, Mackey, Jauch, Piron, Abramsky, and Coecke.

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