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Axioms for the category of Hilbert spaces

Category Theory 2022-06-08 v3 Quantum Physics

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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Cite

@article{arxiv.2109.07418,
  title  = {Axioms for the category of Hilbert spaces},
  author = {Chris Heunen and Andre Kornell},
  journal= {arXiv preprint arXiv:2109.07418},
  year   = {2022}
}

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11 pages