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Interpreting Quantum Theories$
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Laura Ruetsche

Print publication date: 2011

Print ISBN-13: 9780199535408

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199535408.001.0001

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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 18 January 2022

Extraordinary Qm

Extraordinary Qm

(p.148) 7 Extraordinary Qm
Interpreting Quantum Theories

Laura Ruetsche

Oxford University Press

This chapter highlights other surprising aspects of QM: unlike theories of ordinary QM, theories of QM can traffic in algebras none of whose countably additive states are pure. The chapter sketches and provides simple illustrations of the mathematical basis of this circumstance: atomless von Neumann algebras. It also illustrates the uses to which atomless von Neumann algebras are put in QM.

Keywords:   non-atomic von Neumann algebras, type theory, modular theory, Type III factors, KMS states, normal state, pure state, mixed state, unitary inequivalence

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