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The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis

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Quantum and Stochastic Mathematical Physics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 377))

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Abstract

I give a survey of Sergio Albeverio’s work in nonstandard analysis, covering applications to operator theory, stochastic analysis, Dirichlet forms, quantum mechanics, and quantum field theory, and making an attempt at putting his contributions into the historical context of what has happened in the field before and since.

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Notes

  1. 1.

    Actually there isn’t just one set of hyperreals, but infinitely many, but for the purpose of this paper it doesn’t matter much which one we choose as long as it is sufficiently rich (in technical terminology, it should be \(\aleph _1\)-saturated).

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  1. Department of Mathematics, University of Oslo, PO Box 1053, 0316, Blindern, Oslo, Norway

    Tom Lindstrøm

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  1. Faculty of Technology, Linnaeus University, Växjo, Sweden

    Astrid Hilbert

  2. Department of Economics, Insubria University, Varese, Italy

    Elisa Mastrogiacomo

  3. Department of Mathematics, University of Trento, Povo, Trento, Italy

    Sonia Mazzucchi

  4. Applied Mathematics / Stochastic, University of Wuppertal, Wuppertal, Germany

    Barbara Rüdiger

  5. Department of Mathematics, University of MIlan, Milano, Italy

    Stefania Ugolini

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Lindstrøm, T. (2023). The Allure of Infinitesimals: Sergio Albeverio and Nonstandard Analysis. In: Hilbert, A., Mastrogiacomo, E., Mazzucchi, S., Rüdiger, B., Ugolini, S. (eds) Quantum and Stochastic Mathematical Physics. Springer Proceedings in Mathematics & Statistics, vol 377. Springer, Cham. https://doi.org/10.1007/978-3-031-14031-0_9

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