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Notions of Infinity in Quantum Physics

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Classical and Quantum Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 229))

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Abstract

In this article we will review some notions of infiniteness that appear in Hilbert space operators and operator algebras. These include proper infiniteness, Murray von Neumann’s classification into type I and type III factors and the class of Følner C*-algebras that capture some aspects of amenability. We will also mention how these notions reappear in the description of certain mathematical aspects of quantum mechanics, quantum field theory and the theory of superselection sectors. We also show that the algebra of the canonical anti-commutation relations (CAR-algebra) is in the class of Følner C*-algebras.

Dedicated to Alberto Ibort on the occasion of his 60th birthday.

Supported by research projects MTM2017-84098-P and Severo Ochoa SEV-2015-0554 of the Spanish Ministry of Economy and Competition (MINECO), Spain.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University Carlos III Madrid, Avda. de la Universidad 30, 28911, Leganés, Madrid, Spain

    Fernando Lledó & Diego Martínez

  2. Instituto de Ciencias Matemáticas (ICMAT), C/ Nicolás Cabrera 13-15, 28049, Madrid, Spain

    Fernando Lledó & Diego Martínez

Authors
  1. Fernando Lledó
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  2. Diego Martínez
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Correspondence to Fernando Lledó .

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Editors and Affiliations

  1. Università degli Studi di Napoli Federico II, Naples, Italy

    G. Marmo

  2. Institute of Mathematical Sciences (ICMAT), Madrid, Spain

    David Martín de Diego

  3. Universitat Politècnica de Catalunya, Barcelona, Spain

    Miguel Muñoz Lecanda

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Lledó, F., Martínez, D. (2019). Notions of Infinity in Quantum Physics. In: Marmo, G., Martín de Diego, D., Muñoz Lecanda, M. (eds) Classical and Quantum Physics. Springer Proceedings in Physics, vol 229. Springer, Cham. https://doi.org/10.1007/978-3-030-24748-5_14

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