In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 263 (2011)

Laura Ruetsche
University of Michigan, Ann Arbor
John Earman
University of Pittsburgh
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.
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Quantum Bayesianism Assessed.John Earman - unknown - The Monist 102 (4):403-423.
A New Problem for Quantum Mechanics.Alexander Meehan - forthcoming - British Journal for the Philosophy of Science:000-000.
Why Be Normal?Laura Ruetsche - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (2):107-115.

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