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Applications of Generalized B∗-Algebras to Quantum Mechanics

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Positivity and its Applications

Part of the book series: Trends in Mathematics ((TM))

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Abstract

In this paper, we discuss quantum mechanical systems of which the observables are represented by self-adjoint elements of a GB∗-algebra. More specifically, we investigate the phenomenon of quantum entanglement within this framework. Motivated by this, we also give results on pure states of GB∗-algebras, and provide an integral representation theorem for states of nuclear metrizable locally convex quasi ∗-algebras.

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Acknowledgements

1. This work is wholly supported by the National Research Foundation of South Africa (NRF).

2. The author expresses his gratitude to Prof Nadia Boudi of the Mohammed V University in Rabat, Morocco, for bringing references [16] and [20] to his attention.

3. The author expresses his sincere gratitude to the referee for a very careful reading of the manuscript and for his/her numerous suggestions which greatly improved the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Nelson Mandela University, Port Elizabeth, South Africa

    Martin Weigt

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  1. Martin Weigt
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Correspondence to Martin Weigt .

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Editors and Affiliations

  1. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Eder Kikianty

  2. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Mokhwetha Mabula

  3. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Miek Messerschmidt

  4. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Jan Harm van der Walt

  5. Department of Mathematics, University of Pretoria, Hatfield, South Africa

    Marten Wortel

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Weigt, M. (2021). Applications of Generalized B∗-Algebras to Quantum Mechanics. In: Kikianty, E., Mabula, M., Messerschmidt, M., van der Walt, J.H., Wortel, M. (eds) Positivity and its Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-70974-7_16

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