From Operator Algebras to Complexity Theory and Back
- Creators
-
Vidick, Thomas
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.
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.Additional details
- Eprint ID
- 104618
- DOI
- 10.1090/noti1980
- Resolver ID
- CaltechAUTHORS:20200728-152043230
- Institute for Quantum Information and Matter (IQIM)
- PHY-1125565
- NSF
- GBMF-12500028
- Gordon and Betty Moore Foundation
- CCF-1553477
- NSF
- FA9550-16-1-0495
- Air Force Office of Scientific Research (AFOSR)
- Canadian Institute for Advanced Research (CIFAR)
- Created
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2020-07-28Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter