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Complementarity and Stochastic Independence

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Analysis and Operator Theory

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 146))

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Abstract

A mathematical approach to the notion of complementarity in quantum physics is described and its historical development is shortly reviewed. After that, the notion of n-complementarity is introduced as a natural extension of complementarity and at the same time as weak form of stochastic independence. Several examples in which n-complementarity is realized but not independence are produced. The construction of these examples is based on the structure of Interacting Fock Space (IFS) that is strictly related to the classical theory of orthogonal polynomials. A brief description of both this notion and this connection is included to make the paper self-contained.

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Author information

Authors and Affiliations

  1. Centro Vito Volterra, Università di Roma Tor Vergata, 00133, Rome, Italy

    Luigi Accardi

  2. Department of Mathematics, University of Bari Aldo Moro, Campus of University Ernesto Quagliariello, Via Edoardo Orabona 4, 70126, Bari, Italy

    Yun-Gang Lu

Authors
  1. Luigi Accardi
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  2. Yun-Gang Lu
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Correspondence to Yun-Gang Lu .

Editor information

Editors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Institute of Mathematics, Aix-Marseille University, Marseille, France

    Valentin A. Zagrebnov

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Accardi, L., Lu, YG. (2019). Complementarity and Stochastic Independence. In: Rassias, T.M., Zagrebnov, V.A. (eds) Analysis and Operator Theory . Springer Optimization and Its Applications, vol 146. Springer, Cham. https://doi.org/10.1007/978-3-030-12661-2_1

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