Chapter

Interpreting Probabilities in Quantum Field Theory and Quantum Statistical Mechanics

Laura Ruetsche and John Earman

in Probabilities in Physics

Published in print September 2011 | ISBN: 9780199577439
Published online September 2011 | e-ISBN: 9780191730603 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199577439.003.0010
Interpreting Probabilities in Quantum Field Theory and Quantum Statistical Mechanics

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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 projection operators in the case of quantum mechanics. However, relativistic quantum field theory and the thermodynamic limit of quantum statistical mechanics make extensive use of von Neumann algebras of more general types. This chapter addresses the question whether interpretations of quantum probability devised in the usual manner continue to apply in the more general setting. Features of non-type I factor von Neumann algebras are cataloged. It is shown that these novel features do not cause the familiar formalism of quantum probability to falter, since Gleason's Theorem and the Lüders Rule can be generalized. However, the features render the problem of the interpretation of quantum probability more intricate.

Keywords: probabilities; von Neumann algebra; atoms; quantum field theory; quantum statistical mechanics; minimal projection operator; Gleason's Theorem; Lüders Rule

Chapter.  14542 words. 

Subjects: Philosophy of Science

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