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From Operator Algebras to Complexity Theory and Back

Vidick, Thomas (2019) From Operator Algebras to Complexity Theory and Back. Notices of the American Mathematical Society, 66 (10). pp. 1618-1627. ISSN 0002-9920. https://resolver.caltech.edu/CaltechAUTHORS:20200728-152043230

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Abstract

Quantum mechanics and the theory of operator algebras have been intertwined since their origin. In the 1930s [20] von Neumann laid the foundations for the theory of (what are now known as) von Neumann algebras with the explicit goal of establishing Heisenberg’s matrix mechanics on a rigorous footing (quoting from the preface, in the translation by Beyer: “The object of this book is to present the new quantum mechanics in a unified representation which, so far as it is possible and useful, is mathematically rigorous”). Following the initial explorations of Murray and von Neumann, the new theory took on a life of its own, eventually leading to multiple applications unrelated to quantum mechanics, such as to free probability or noncommutative geometry.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/noti1980DOIArticle
ORCID:
AuthorORCID
Vidick, Thomas0000-0002-6405-365X
Additional Information:© 2019 American Mathematical Society. The author gratefully acknowledges support from the IQIM, an NSF Physics Frontiers Center (NSF Grant PHY-1125565) with support of the Gordon and Betty Moore Foundation (GBMF-12500028), NSF CAREER Grant CCF-1553477, AFOSR YIP award number FA9550-16-1-0495, and a CIFAR Azrieli Global Scholar award. I am indebted to Volkher Scholz, William Slofstra, Henry Yuen, and the Notices referees for multiple comments that greatly improved the presentation of this article.
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-12500028
NSFCCF-1553477
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0495
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:20200728-152043230
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200728-152043230
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104618
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Jul 2020 22:42
Last Modified:28 Jul 2020 22:42

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