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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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