Notions of Infinity in quantum physics

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 amenabili...

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Bibliographic Details
Authors: Lledó, Fernando, Martínez, Diego
Format: other
Status:Versión enviada para evaluación y publicación
Publication Date:2019
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/197445
Online Access:http://hdl.handle.net/10261/197445
Access Level:Open access
Description
Summary: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.

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