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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Detalhes bibliográficos
Autores: Lledó, Fernando, Martínez, Diego
Formato: otro
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/197120
Acesso em linha:http://hdl.handle.net/10261/197120
Access Level:acceso abierto
Palavra-chave:Amenability
Proper infiniteness
Quantum Physics
CAR-algebra
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spelling Notions of infinity in quantum physicsLledó, FernandoMartínez, DiegoAmenabilityProper infinitenessQuantum PhysicsCAR-algebraIn 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.Supported by research projects MTM2017-84098-P and Severo Ochoa SEV-2015-0554 of the Spanish Ministry of Economy and Competition (MINECO), Spain.Peer reviewedSpringer NatureAgencia Estatal de Investigación (España)Ministerio de Economía y Competitividad (España)Ministerio de Ciencia, Innovación y Universidades (España)201920192019info:eu-repo/semantics/otherhttp://purl.org/coar/resource_type/c_3248Postprintinfo:eu-repo/semantics/acceptedVersioninfo:eu-repo/semantics/bookParthttp://hdl.handle.net/10261/197120reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-84098-Pinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0554https://doi.org/10.1007/978-3-030-24748-5_14Noinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1971202026-05-22T06:33:51Z
dc.title.none.fl_str_mv Notions of infinity in quantum physics
title Notions of infinity in quantum physics
spellingShingle Notions of infinity in quantum physics
Lledó, Fernando
Amenability
Proper infiniteness
Quantum Physics
CAR-algebra
title_short Notions of infinity in quantum physics
title_full Notions of infinity in quantum physics
title_fullStr Notions of infinity in quantum physics
title_full_unstemmed Notions of infinity in quantum physics
title_sort Notions of infinity in quantum physics
dc.creator.none.fl_str_mv Lledó, Fernando
Martínez, Diego
author Lledó, Fernando
author_facet Lledó, Fernando
Martínez, Diego
author_role author
author2 Martínez, Diego
author2_role author
dc.contributor.none.fl_str_mv Agencia Estatal de Investigación (España)
Ministerio de Economía y Competitividad (España)
Ministerio de Ciencia, Innovación y Universidades (España)
dc.subject.none.fl_str_mv Amenability
Proper infiniteness
Quantum Physics
CAR-algebra
topic Amenability
Proper infiniteness
Quantum Physics
CAR-algebra
description 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.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019
2019
dc.type.none.fl_str_mv info:eu-repo/semantics/other
http://purl.org/coar/resource_type/c_3248
Postprint
info:eu-repo/semantics/acceptedVersion
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format other
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/197120
url http://hdl.handle.net/10261/197120
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-84098-P
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0554
https://doi.org/10.1007/978-3-030-24748-5_14
No
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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