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Interpreting Probabilities in Quantum Field Theory and Quantum Statistical Mechanics

Laura Ruetsche and John Earman

in Probabilities in Physics

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199577439
eISBN:
9780191730603
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199577439.003.0010
Subject:
Philosophy, Philosophy of Science, Metaphysics/Epistemology

Philosophical accounts of quantum theory commonly suppose that the observables of a quantum system form a Type-I factor von Neumann algebra. Such algebras always have atoms, which are minimal ... More


Representation Without Taxation: An Unstrenuous Tour of Algebraic Notions

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0004
Subject:
Philosophy, Philosophy of Science

This chapter aspires to be an unpunishing introduction to mathematical notions useful for framing and pursuing foundational questions that arise from the unitary inequivalent representations ... More


Operator Algebras and Their Modules: An operator space approach

David P. Blecher and Christian Le Merdy

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198526599
eISBN:
9780191712159
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526599.001.0001
Subject:
Mathematics, Pure Mathematics

This book presents the general theory of algebras of operators on a Hilbert space, and the modules over such algebras. The new theory of operator spaces is presented early on and the text assembles ... More


Extraordinary Qm

Laura Ruetsche

in Interpreting Quantum Theories

Published in print:
2011
Published Online:
September 2011
ISBN:
9780199535408
eISBN:
9780191728525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199535408.003.0007
Subject:
Philosophy, Philosophy of Science

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 ... More


Algebraic Tools

Robert Alicki and Mark Fannes

in Quantum Dynamical Systems

Published in print:
2001
Published Online:
February 2010
ISBN:
9780198504009
eISBN:
9780191708503
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504009.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces an abstract algebraic language unifying the description of classical systems, finite quantum systems, and infinite ones, the last appearing in particle and statistical ... More


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