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Quantum Probability Theory and the Foundations of Quantum Mechanics

  • Jürg FröhlichEmail author
  • Baptiste Schubnel
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 899)

Abstract

By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop “quantum probability theory” into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the “foundations of quantum mechanics”, using mathematical tools from “quantum probability theory” (such as the theory of operator algebras).

Keywords

Quantum Mechanic Physical System Physical Quantity Pure State Operator Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes

Acknowledgements

A rough first draft of this paper has been written during J.F.’s stay at the School of Mathematics of the Institute for Advanced Study (Princeton), 2012/2013. His stay has been supported by the ‘Fund for Math’ and the ‘Monell Foundation’. He is deeply grateful to Thomas C. Spencer for his most generous hospitality. He acknowledges useful discussions with Ph. Blanchard, P. Deift, S. Kochen and S. Lomonaco. He thanks D.Bernard for drawing his attention to [6] and W. Faris for correspondence. He is grateful to D. Buchholz, D. Dürr, S. Goldstein, J. Yngvason and N. Zanghi for numerous friendly and instructive discussions, encouragement and for the privilege to occasionally disagree in mutual respect and friendship.

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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut für Theoretische Physik, HIT K42.3, ETH ZürichZürichSwitzerland
  2. 2.Departement MathematikETH ZürichZürichSwitzerland

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